SOLUTION: The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of the painting? A. 9 inches B. 12 inches C. 1

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Question 939239: The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of the painting?
A.
9 inches
B.
12 inches
C.
13 inches
D.
18 inches
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The length L of a rectangular painting is 3in longer than its width W.
L=W%2B3in
If the diagonal d=15in long, what is the length L of the painting?
use Pythagorean theorem since the length, the width, and the diagonal of the rectangle form right triangle
d%5E2=L%5E2%2BW%5E2
%2815%29%5E2=%28W%2B3%29%5E2%2BW%5E2...solve for W
225=W%5E2%2B6W%2B9%2BW%5E2
0=2W%5E2%2B6W%2B9i-225
0=2W%5E2%2B6W-216....divide by 2
0=W%5E2%2B3W-108 ...factor, write 3W as -9W%2B12W
W%5E2-9W%2B12W-108...group
%28W%5E2-9W%29%2B%2812W-108%29...factor
W%28W-9%29%2B12%28W-9%29
%28W%2B12%29%28W-9%29=0
solutions:
if %28W%2B12%29=0=> W=-12...since we are looking for a width we cannot use negative solution
if %28W-9%29=0=>highlight%28W=9in%29...this is our solution
now find the length
L=W%2B3in
L=9in%2B3in
highlight%28L=12in%29
and your answer is
B.
12 inches