Can anyone help me with these few questions?

Question

A construction company is planning to pour concrete for a driveway. The length of the driveway is 16 ft longer than its width 'w'.
Find the dimensions of the driveway if it has an area of 260 sq ft.

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the result by the same amount in each dimension to post on her web site. Janeel wants the area of the image to be one eighth that of the original photograph.
1.Write an equation to represent the area of the reduced image.
2.Find the dimensions of the reduced image.

Answer 1

1) Let w = width of the driveway.
Since the length of the driveway is 16 feet longer than the width, it follows that w + 16 is the width.

The formula for the area of the driveway is given by
A = (length) x (width), which we know the values of
A = (w + 16) w
A = w^2 + 16w

It is also given that the driveway has an area of 260 square feet. That means A = 260, and we can plug this value in for A.

260 = w^2 + 16w

Now, let's move 260 over to the right hand side, giving us

0 = w^2 + 16w - 260

At this point, we factor this.

0 = (w + 26) (w - 10)

Giving us two solutions: w = -26, w = 10
However, since the width of a driveway can never be negative, we reject w = -26, and keep w = 10.

Now that we know the width, we can obtain the length; after all, it was given to be 16 feet longer than the width. Therefore, the length is 10 + 16 = 26.

So the dimensions of the driveway are 10 feet by 26 feet.

Answer 2

A construction company is planning to pour concrete for a driveway. The length of the driveway is 16 ft longer than its width 'w'.
Find the dimensions of the driveway if it has an area of 260 sq ft.

260ft^2=w(w+16)-w^2+16w
w^2+16w-260=0
(w+26)(w-10)=0
w>0
w=10ft
l=26ft

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the result by the same amount in each dimension to post on her web site. Janeel wants the area of the image to be one eighth that of the original photograph.
1.Write an equation to represent the area of the reduced image.
2.Find the dimensions of the reduced image.

10*12=120 in^2
120/8=15in^2
(10-x)(12-x)=15
120-22x+x^2=15
x^2-22x+105=0
(x-7)(x-15)=0
x=7, 15
10-x>0
only 7 is physically possible
10-7=3
12-7=5
new dimensions are 3"5"

Answer 3

OK, for the first, you just need to write an equation.
area = width times length
Then fill in the numbers you know:
260 = w * l
What else do you know?
l = w + 16
so now you have
260 = w * (w+16) = w^2 + 16w
or, w^2 + 16w - 260 = 0
Now you just need to find the roots, using the quadratic equation, or make guesses at factors of 260, which is what I just did. 260=26*10, and the difference between 26 and 10 is 16!
So, try (w-10)*(w+16) = 0
and that works!
So the possible solutions are w=10 and w=-16. But -16 doesn't make any sense for a width of something, so it must be 10!

For the second, again you just have to read carefully, write sentences, and then fill in the numbers.
The area is 1/8 of the original means
A = original/8
well, original = 10x12
so A = 10x12/8 is an equation that represents the area of the reduced image.
For the dimensions, you simply take the square root of 8 times the length of each dimension!

Answer 4

I can help with the first one:
1)w=the width
w+16=the length
260=the area

260=w(w+16)
w^2+16w=260
w^2+16w-260=0
(w+26)(w-10)=0
w=10 or -26
We throw out the -26 and use 10.
10+16=26

The dimensions are 10 ft. by 26 ft.

Answer 5

w = width
le length =w=16
a= l*w = w(w+16) = w^2+16w
so w^2+16 w = 260
w^2 +16w -260 =0
(w+26)(w-10) = 0
w - 10 = 0
w=10
so l = w+16 = 16+10 = 26

w/l = 10/12 = 5/6
wl = 120(1/8)= 15
so l =15/w
Substitute this in 1st equation to get:
w/(15/w)= 5/6
w^2/15 = 5/6
w^2= 15(5/6) =75/6 = 25/2
w = (w = approximately 5/1,414= 3.53 in
l= 15/w =15/3.53= 4.25 in

Answer 6

problem 1

A = LW

260 = (w + 16)(w)

260 = w² + 16w

260 - 260 = w² + 16w - 260

0 = w² + 16w - 260

0 = (w + 26) (w - 10)

- - - - - - - -

Roots

w = - 26. . < = .Not used

w = 10

- - - - - - - -

The width is 10 feet

The length is w + 16 or 10 + 16 = 26

The length is 26 feet

- - - - - - - - - - - - - -

Check

Area = LW

260 = 26 x 10

260 = 260

- - - - - - - -s-

Answer 7

The first one, the dimensions are 26 by 10.

Answer 8

1)
(w+16).w=260

w^2+16w-260=0

width=w=12

length=w+16=12+16=28

2)

equation=ratio*width*length
=1/8 * 12*10

12*1/8=3/4
length=12-3/4=45/4

10*1/8= 5/4
10-5/4=35/4