SOLUTION: The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 84 m2, how long is the diagonal? Round your answer to the neare

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Question 973872: The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 84 m2, how long is the diagonal? Round your answer to the nearest tenth.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 84 m2, how long is the diagonal? Round your answer to the nearest tenth.
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let x=length of diagonal
x-3=length of rectangle
x-8=width of rectangle
..
length*width=area
(x-3)(x-8)=84
x^2-11x+24=84
x^2-11x-60=0
(x-15)(x+4)=0
x=15
how long is the diagonal? 15 m
numbers do not check:
By the pythagorean theorem:
length^2+width^2=diagonal^2
12^2+7^2≠15^2
144+49≠15^2
193≠225