i have three problems anybody help me?

Question

Find a rectangle whose area is greater than its perimeter. What are its dimensions?

Find a rectangle whose perimeter is larger than its area . What are its dimensions?


Find the cost per ounce of a sunscreen made from 80 oz of a lotion that costs $3.00per ounce and 20oz of a lotion that costs $8.50.

Answer 1

P = 2L + 2W

P = 2(7) + 2(5)

P = 14 + 10

P = 24

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Area formula

A = L x W

A = 7 x 5

A = 35

Area is larger

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2.

P = 2L + 2W

P = 2(3) + 2(2)

P = 6 + 4

P = 10

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A = L x W

A = 3 x 2

A = 6
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Perimeter is larger

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Answer 2

1) Rectangle whose area is greater than its perimeter. What are the dimensions?

Area of rectangle = b times h where b = base, h = height
Perimeter = b + b + h + h or 2b + 2h or 2(b + h)
Rectangle = 2 opposite sides are equal. By this definition, a square is a rectangle, whose four sides are equal.

Where is the AREA equals the PERIMETER?

(b x h) = 2 (b + h)
(b x h) - 2(b + h) = 0
From the above equation, we can see that the only instance it will be true is when b = 4 and h = 4 such that,
(4 x 4) - 2 (4 + 4) = 0
16 - 2(8) = 0
16 - 16 = 0
0 = 0

From this, we can deduce that the Area of a rectangle is greater than its perimeter if the sum of b and h is greater than 8, or b + h is equal or greater than 9.
b and h can be ( 4, 5 ), (5,4), (5,5) , (5,6) , (6,5) and soon.
In this case, Area = 20, Perimeter = 18 (For b=4, h =5)
Area = 25, Perimeter = 20 ( For b = 5, h = 5)


2) Rectangle whose perimeter is greater than its area.

From 1) we can say that the perimeter of a rectangle is greater than its area if ( b + h) is lesser than 8.
For b = 3, h = 4 ===> Area = 12, Perimeter = 14
b = 3, h = 3 ===> Area = 9, Perimeter = 12
b = 3, h = 2 ===> Area = 6 . Perimeter = 10

3) Cost per ounce of sunscreen made from 80 oz of lotion that costs $ 3.00 per ounce and 20 oz of a lotion that costs $ 8.50

Total Cost of lotion A = 80 oz times $ 3.00/oz = $ 240.00
Total Cost of lotion B = 20 oz = 8.50

Total Cost of Sunscreen = $ 240 + 8.50 = $ 248.50
Since there are 100 oz total, the cost of the suncreen is
$ 248.50/ 100 oz = $ 2.485 per ounce

However if lotion B is $ 8.50 per ounce instead of just $ 8.50,
the total cost of the sunscreen is
80 oz x $ 3.00 + 20 oz x $ 8.50 = $ 240 + 170 = $ 410.00
Therefore, cost per ounce is $410/100 oz = $ 4.10

Answer 3

Find a rectangle whose area is greater than its perimeter. What are its dimensions? You mean No. Indicating these ? as units of both are different.
There are so many dimensions
L = 8 B = 3
Area = 8 × 3 = 24 sq. units
Perimeter = 2(8 + 3) = 22 units
area > perimeter

Find a rectangle whose perimeter is larger than its area . What are its dimensions?
You mean No. Indicating these ? as units of both are different.
L = 4 B = 3
Area = 4 × 3 = 12 sq. units
Perimeter = 2(4 + 3) = 14 units
perimeter > area


Find the cost per ounce of a sunscreen made from 80 oz of a lotion that costs $3.00per ounce and 20oz of a lotion that costs $8.50.
You have find average
Total cost = 80 × 3 + 20 × 8.50
= = $ 240 + $ 170 = $ 410
Total wt. = 80 + 20 = 100 oz
Therefore Average cost = 410 / 100 = 4.10 $ per oz.

Answer 4

1) Rectangle whose area is greater than its perimeter. What are the dimensions?

Area of rectangle = b times h where b = base, h = height
Perimeter = b + b + h + h or 2b + 2h or 2(b + h)
Rectangle = 2 opposite sides are equal. By this definition, a square is a rectangle, whose four sides are equal.

Where is the AREA equals the PERIMETER?

(b x h) = 2 (b + h)
(b x h) - 2(b + h) = 0
From the above equation, we can see that the only instance it will be true is when b = 4 and h = 4 such that,
(4 x 4) - 2 (4 + 4) = 0
16 - 2(8) = 0
16 - 16 = 0
0 = 0

From this, we can deduce that the Area of a rectangle is greater than its perimeter if the sum of b and h is greater than 8, or b + h is equal or greater than 9.
b and h can be ( 4, 5 ), (5,4), (5,5) , (5,6) , (6,5) and soon.
In this case, Area = 20, Perimeter = 18 (For b=4, h =5)
Area = 25, Perimeter = 20 ( For b = 5, h = 5)


2) Rectangle whose perimeter is greater than its area.

From 1) we can say that the perimeter of a rectangle is greater than its area if ( b + h) is lesser than 8.
For b = 3, h = 4 ===> Area = 12, Perimeter = 14
b = 3, h = 3 ===> Area = 9, Perimeter = 12
b = 3, h = 2 ===> Area = 6 . Perimeter = 10

3) Cost per ounce of sunscreen made from 80 oz of lotion that costs $ 3.00 per ounce and 20 oz of a lotion that costs $ 8.50

Total Cost of lotion A = 80 oz times $ 3.00/oz = $ 240.00
Total Cost of lotion B = 20 oz = 8.50

Total Cost of Sunscreen = $ 240 + 8.50 = $ 248.50
Since there are 100 oz total, the cost of the suncreen is
$ 248.50/ 100 oz = $ 2.485 per ounce

However if lotion B is $ 8.50 per ounce instead of just $ 8.50,
the total cost of the sunscreen is
80 oz x $ 3.00 + 20 oz x $ 8.50 = $ 240 + 170 = $ 410.00
Therefore, cost per ounce is $410/100 oz = $ 4.10

Answer 5

1.
Perimeter = b + b + h + h or 2b + 2h or 2(b + h)
In a rectangle, opposite sides are equal. (By this definition, a square is a rectangle, whose four sides are equal)

First find the condition, where the area and its perimeter are equal.
Area = Perimeter
(b x h) = 2(b + h)
bh - 2(b + h) = 0
The above equation is only true when both lenght and height are equal to 4 units
(4 x 4) - 2 (4 + 4) = 0
16 - 2(8) = 0
16 - 16 = 0
0 = 0

Therefore, the Area of a rectangle is greater than its perimeter if the sum of b and h is greater than 8, or b + h is equal or greater than 9. i.e
b and h can be ( 4, 5 ), (5,4), (5,5) , (5,6) , (6,5) and soon.

In this case,
Area = 20, Perimeter = 18 (For b=4, h =5)
Area = 25, Perimeter = 20 ( For b = 5, h = 5)


2
If a and b are the sides of the rectangle, you can find a number of values like this

The perimeter i.e 2(a+b) > area i.e
ab
or
ab < 2(a+b)
or
ab/(a+b) should be < 2

Taking some values
a = 1, b = 2,
2/3 is <2 and

perimeter = 3*2=6 ; area = 2


a=1 b=5
5/6 is <2

primeter = 6*2 =12 ; area = 5
and so on .........

.

Answer 6

area of any rectangle, with sides a and b, equals : S = a*b.
Perimeter of any rectangle is sum of all sides. P = a+a+b+b = 2*a + 2*b.
the first question. area greater than perimeter. then S>P.
take S and P formulas from above and write :
a*b>2*a+2*b;
a*b-2*a>2*b;
a(b-2)>2*b;
a>2*b / (b-2). (if b-2 > 0).
a<2*b / (b-2). (if b-2 <0).
this last two formulas represents all rectangles, whose area is bigger, than perimeter. you can take b freely and then calculate a. if you take , say, b=3, then b-2 = 1, 1>0, then use 1 formula and get: a>2*3 / (3-2) => a>6. that means that every rectangle vith sides 3*7, 3*8, 3*9 and so on will have square bigger than perimeter: 3*7 > 3+3+7+7; 3*8>3+3+8+8 and so on. if you take b-2 < 0, then b<2. but side of rectangle can't be negative. then it can be greater than zero and smaller than 2. it can be 0.1; 0.2...1...1.2...1.99 and so on. if b = 1, then use second formula. then a<2*1(1-2) => a<-2. you can see that a is negative in second formula case. then, you must use only first formula.

when perimeter is larger than area, you write:
P>S;
2*a+2*b>a*b;
2*a - a*b > -2*b;
a(2-b) > -2*b;
a(b-2) < 2*b;
a< 2*b /(b-2) (if b-2 > 0);
a> 2*b /(b-2) (if b-2 <0).
now, if use first formula, and freely take b = 4, then
a<2*4 / (4-2) => a<4. a can be 3, 2, 1. then P>S, because 4+4+3+3 > 4*3; 4+4+2+2> 4*2, and so on.
last part of your questions answered another friends.

Answer 7

A rectangle with dimensions of 8 and 4 would have perimeter of 24. And the area would be 32. Its greater, right?

Answer 8

1st question: rectangle 5 x 10. Area = 50. Per. = 30.

2nd question: rectangle 1 x 2. Area =2. Per. = 4.

3rd question: I understand it to be that you add the two bottles together to get one bottle of sunscreen? If so:
you would have 100 oz bottle that cost $240.00 (80 x $3) + $170.00 (20 x $8.50) which equals total cost of $410.00.
The 100 oz. bottle cost $410 or $4.10 per oz.

Answer 9

Area is greater than perimeter:
300x300
a=90000
p=1200

Perimeter is greater than area:
1x1
a=1
p=4

8.50bottle/20oz=0.425
The cost per ounce of the 80 ounce bottle is 3 dollars per ounce, whereas the 20 ounce bottle costs 42.5 cents (or 43 cents, rounded) per ounce.

Answer 10

1st ans: 4 and 5(Perimeter = [4+5]*2 = 18 units ; Area = [4*5] = 20 sq units)
2nd ans: 3 and 4Perimeter = [3+4]*2 = 14 units ; Area = [3*4] = 12 sq units)
3rd ans: Duno the definition of 1oz! Sry cnt help u with this one!