SOLUTION: The perimeter of a rectangle is 42cm. if the diagonal is 15cm find the width of the rectangle.

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Question 1065330: The perimeter of a rectangle is 42cm. if the diagonal is 15cm find the width of the rectangle.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
l,w = length, width, respectively
++2l%2B2w+=+42+ (1)
+sqrt%28l%5E2%2Bw%5E2%29+=+15+ (2)
(1) —> l+%2B+w+=+21+ —> +l+=+21-w+
Square both sides of (2):
+l%5E2+%2B+w%5E2+=+225+
Now substitute "21-w" for "l" in this last expression:
+%2821-w%29%5E2+%2B+w%5E2+=+225+
+%28441-21w-21w%2Bw%5E2%29+%2B+w%5E2+=+225+
Combine like terms, and rearrange:
++2w%5E2+-+42w+%2B+216+=+0+
Divide through by 2:
++w%5E2+-+21w+%2B+108+=+0+
Factor:
++%28w-9%29%28w-12%29+=+0+
w = 9 or w = 12
If w = 9, (1) tells us l = 12
if w = 12, (1) tells us l = 9 (<<< discard because convention is l>w for a rectangle)
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Ans:
+highlight%28+length+=+12cm%29, +highlight%28width+=+9cm+%29+
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Check:
Diagonal = sqrt%2812%5E2+%2B+9%5E2%29+=+sqrt%28144%2B81%29+=+sqrt%28225%29+=+15+ (ok)
Perimeter = +2l%2B2w+=+2%2812%29+%2B+2%289%29+=+24%2B18+=+42+ (ok)