SOLUTION: 19. The length of a rectangular plot of land is 7 m greater than its width. The diagonal is 8 m greater than the width of the plot of land. What are the dimensions of the plot

Question 697060: 19. The length of a rectangular plot of land is
7 m greater than its width. The diagonal
is 8 m greater than the width of the plot
of land. What are the dimensions of the
plot of land?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
l = w + 7
d = w + 8
The diagonal is the hypotenuse of a right triangle whose other two legs are the length and width:
l^2 + w^2 = d^2
(w+7)^2 + w^2 = (w+8)^2
Simplify and solve for w:
w^2 - 2w - 15 = 0
This can be factored as (w-5)(w+3) = 0
Take the positive solution, w = 5
So the width is 5 m and the length is 12 m
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