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Question
The length of a rectangle is 7 cm greater than its width and a diagonal of the restangle is 2cm greter than its length. Find the width of the rectangle
Let length of the rectangle is L, the width is W, and the diagonal is D.
The equations that we have are as follows:
(a) L = W+7.
(b) D = L+2
(c) D² = W²+L²
From (b), we can derive (d) D²=(L+2)²=L²+4L+4.
Putting this into (c) for D² gives L²+4L+4=W²+L², which changes to
(e) 4L+4=W² by subtracting off the L² term from both sides of the equation.
We can then put (a) into equation (e) so that we now have
4(W+7)+4=W². This can be changed to (f) W²-4W-32=0.
We can factor (f), giving (W-8)(W+4)=0, so the choices are (g) W=8 and (h) W=-4. Since W is a length, I don't believe I have ever seen -4 on a ruler, so the answer must be (g) W=8.
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Checking this answer gives us L=W+7=15 and D=17 by looking at the first two equations. D²=289, W²=225, and L²=8²=64. Sure enough, this is satisfied as well.
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