rectangular

[yasem77]

A certain rectangular window is twice as long as it is wide. If its perimeter is 10 feet, then its dimensions in feet are

(a) 3/2 by 7/2
(b) 5/3 by 10/3
(c) 2 by 4
(d) 3 by 6
(e) 10/3 by 20/3

Can somebody help? I don´t know how to solve it. Thanks:-)

[ssmiles08]

width = x
length = 2x

perimeter = 2(2x) + 2(x) = 10; 4x + 2x = 10; x = 5/3

length = 2x = 10/3

(B)

[Scott@TargetTestPrep]

A certain rectangular window is twice as long as it is wide. If its perimeter is 10 feet, then its dimensions in feet are

(a) 3/2 by 7/2
(b) 5/3 by 10/3
(c) 2 by 4
(d) 3 by 6
(e) 10/3 by 20/3

Can somebody help? I don�t know how to solve it. Thanks:-)

Solution:

We can set up the dimensions of the rectangular window as w = width and l = length.

We are given that the rectangular window is twice as long as it is wide. Thus, we can say:

l = 2w

We also know that the perimeter is 10 feet, so we substitute this value into the perimeter formula for a rectangle:

2l + 2w = 10

We can now substitute in 2w for l and we have:

2 x 2w + 2w = 10

4w + 2w = 10

6w = 10

w = 10/6 = 5/3

Because we know that the length is twice the width, we know that the length is:

2 x 5/3 = 10/3

Answer:B

[GMATGuruNY]

A certain rectangular window is twice as long as it is wide. If its perimeter is 10 feet, then its dimensions in feet are

(a) 3/2 by 7/2
(b) 5/3 by 10/3
(c) 2 by 4
(d) 3 by 6
(e) 10/3 by 20/3

P = 2W + 2L.
An alternate approach is to PLUG IN THE ANSWERS, which represent the values of W and L.
When the correct answer choice is plugged in, P=10.

Answer choice D: W=3, L=6
Here, P = (2*3) + (2*6) = 18.
Too big.
Eliminate D and E.

Answer choice B: W=5/3, L=10/3
Here, P = 2(5/3) + 2(10/3) = 10/3 + 20/3 = 30/3 = 10.
Success!

The correct answer is B.

[Matt@VeritasPrep]

Another approach:

2L + 2W = 10

L = 2W

Now substitute

2*(2W) + 2W = 10

W = (10/6) = 5/3

L = 2W = 2*(5/3) = 10/3

... and we're done!