SOLUTION: A rectangle has a length which is 14 cm longer than its width. If the diagonal of the rectangle is 34 cm long, what is the perimeter of the rectangle?

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Question 926757: A rectangle has a length which is 14 cm longer than its width. If the diagonal of the rectangle is 34 cm long, what is the perimeter of the rectangle?
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
Let width be w cm
length = (w+14) cm
Diagonal = 34 cm
As per pythagorean theorem ,
+diagonal%5E2+=length%5E2%2Bwidth%5E2%29
+34%5E2+=%28w%2B14%29%5E2%2Bw%5E2
+1156+=%28w%2B14%29%2A%28w%2B14%29+%2Bw%5E2
1156++=w%28w%2B14%29%2B14%28w%2B14%29%2Bw%5E2
+1156++=+w%5E2%2B14w%2B14w%2B196%2Bw%5E2
+1156+=+w%5E2%2B28w+%2B196%2Bw%5E2
1156=+2+w%5E2%2B28+w%2B196
mve 1156 to the right
0+=+2w%5E2+%2B28w%2B196-1156
+0+=+2w%5E2%2B28w-960
divide with 2 each and every term on both sides
+0%2F2+=+%282w%5E2%2F2%29+%2B28w%2F2-960%2F2
0+=+w%5E2%2B14w-480
0+=w%5E2%2B30w-16w-480
0+=w%28w%2B30%29-16%28w%2B30%29
0+=%28w%2B30%29%28w-16%29
possible solution
either (w+30)= 0 or (w-16)=0
w=-30 or w= 16
w cannot be negative
hence w= 16 cm
length = 16+14 = 30 cm
Perimeter =+2%28length%2Bwidth%29
=2%2830%2B16%29
=2%2846%29
= 92 cm
Result : Perimeter = 92 cm