Math Question?

Question

There is a rectangular piece of carpet with a perimeter of 34ft. Another piece is half as long and twice as wide. It's perimeter is 26ft. What are both's dimensions?

Answer 1

L & W are length and width of the first piece

2L + 2W = 34
2(L/2) + 2(2W) = 26

2L + 2W = 34
L + 4W = 26

Multiply bottom equation by -2 and add
2L + 2W = 34
-2L - 8W = -52

-6W = -18
W = 3

2L + 2W = 34
2L + 2(3) = 34
2L = 34 - 6
2L = 28
L = 14

So the first piece is 14 x 3
The second piece is 7 X 6

Answer 2

Well perimeter of a rectangle can be expressed using the equation:

P = 2(L + W)
= 2L+ 2W

so just substitute the 34 in for P for the first equation:

34= 2L +2W

for the second equation we need to modify it a little bit based on the the information provided:

26= (2L/2) + 2(2W)
Simplify: 26=L+4W
Solve for L: L=26+-4W

Now that we know that L=26+-4W we can put that into the other equation:

34= 2(26+-4W) +2W
Simplify: 34= 52+-8W+2W
34= 52+-6W
-18=-6W
W= 3

Now that we know what the width is we can solve for L by using the equation we found:

L=26+-4W
L=26+-4(3)
L=14

So the dimensions of the first one is 14x3

Second one is just simply now simply take those dimensions and divide 14 in half and multiply 3 by 2 and the dimensions are 7x6

Answer: First = 14x3
Second= 7x6

Hope that's helpful!

Answer 3

There is a rectangular piece of carpet with a perimeter of 34ft.

1) 2L + 2W = 34

Another piece is half as long and twice as wide. It's perimeter is 26ft

2) 2(L/2) + 2(2W) = 26
L + 4W = 26
L = 26 - 4W

1) 2(26 - 4W) + 2W = 34
52 - 8W + 2W = 34
- 6W = - 18
W = 3

L = 26 - 4(3) = 26 - 12 = 14

Dimensions are 3 by 14 and 6 by 7

Answer 4

They give the shape as rectangular so the general formula is 2A + 2B = Perimeter

EQ1: 2A + 2B = 34

They give another carpet in terms of the first carpet and perimeter:

EQ2: 2a + 2b = 26

a=2A
b=1/2 B
Plug into EQ2: 2(2A) + 2(1/2 B) = 26
4A +B =26
B= 26-4A

Plug into EQ1:
2A + 2( 26-4A) = 34
2A + 52 -8A = 34
6A=18
A= 3
B= 26- 4(3)= 26-12=14

First Carpet A=3 B=14; 3 x 14
Second Carpet: a=2A=6, b= 1/2 B =7; 6 x 7

Answer 5

carpet 1: x=width; y=length
carpet 2: 2x=width: y/2=length

rectangular perimeter = 2*width + 2*length
carpet 1: 34 = 2 * x + 2 * y ==> 34=2x+2y
carpet 2: 26= 2 * 2x + 2 * y/2 ==> 26=4x+y

solve system (substitution method)
rearange carpet 2 => y=26-4x
substitue into carpet 1 => 34 = 2x+2(26-4x)
34=2x+52-8x
-18=-6x
x=3

place x=3 in either equation and solve for y
carpet 2: 4x+y=26 => 4(3) +y =26 => 12+y=26
y=14

carpet dimensions
carpet 1: x=width; y=length ====> 3ft x 14ft
carpet 2: 2x=width: y/2=length ==> 6ft x 7ft

Answer 6

let x be the long side ,y the wide side of rectangular piece of carpet you first equation 2(x+y)=34 the other piece has 1/2x long and 2y wide the second equation is 2(1/2x+2y)=26. solving the system of the two equations you will get x=17 and y=3.

Answer 7

Let the dimensions of the first piece be X long and Y wide.
Then 2X + 2Y = 34
The second piece has dimensions X/2 and 2Y
Then 2(X/2) +2(2Y) = 26
or X+4Y =26
or X = 26 -4Y plug this into the first equation
2(26-4Y)+2Y =34
52-8Y+2Y=34
-6Y= 34-52
-6Y=-18
Y=3
and X = 14

First piece is 14 x 3, second 7 x 6

Answer 8

2l +2w = 34 (1)
l +4w = 26 (2)
-2l -8w -52 (3) = -4*(2)
-6w -18
w = 3
l = (34-2w)/2 = 14
first piece = 14 X 3
2nd piece 7 x 6

Answer 9

First Carpet

Perimeter = (2 l ) + (2 w) = 34............ Eq 1

Second Carpet

Perimeter = l + 4 w = 26........................Eq 2


Make Eq 2 l term same as eq 1 l term (Multiply by 2)

2 l + 8w = 52 .......................Eq 3
Subtract Eq 3 - Eq 1

6w = 18
w = 3
Substitute in Eq 1

2l + 6 = 34

2l = 28
l = 14
So First Carpet is

14 feet Long and 3 feet Wide

Second Carpet is

7 feet Long and 6 feet Wide