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:-)
rectangular
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Solution:yasem77 wrote: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:-)
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
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P = 2W + 2L.yasem77 wrote: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
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.
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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!
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!