SOLUTION: The length of a rectangle is 7 m more than the width. The length of a diagonal is 13 m. Find the length.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The length of a rectangle is 7 m more than the width. The length of a diagonal is 13 m. Find the length.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 204754: The length of a rectangle is 7 m more than the width. The length of a diagonal is 13 m. Find the length.
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
rectangle's length = L
rectangle's width = W
rectangle's diagonal = D

L = 7 + W
D = 13
use the Phytagoras formula:
D%5E2+=+L%5E2+%2B+W%5E2
13%5E2+=+%287+%2B+W%29%5E2+%2B+W%5E2
169+=+49+%2B+14W+%2B+W%5E2+%2B+W%5E2
0+=+49+%2B+14W+%2B+W%5E2+%2B+W%5E2+-+169
0+=+2W%5E2+%2B+14W+%2B+-+120
divide each side by 2
0+=+W%5E2+%2B+7W+%2B+-+60
factorize it:
0 = (W + 12)(W - 5)
W + 12 = 0 --> W = -12
or
W - 5 = 0 --> W = 5

W = 5 is used because the width of a rectangle must not be a negative value
L = 7 + W = 7 + 5 = 12

so, the length of the rectangle is 12 m