Posted by sydney on Monday, December 19, 2011 at 8:54pm.
The structure of the problem should give yu a hint. The diagonal of a rectangle forms a right triangle with the sides. So, think Pythagorean Theorem.
If the length is x and the width is y,
(y+70)^2 + y^2 = 130^2
y^2 + 140y + 4900 + y^2 = 16900
2y^2 + 140y - 1200 = 0
y^2 + 70y - 6000 = 0
(y-50)(y+120) = 0
y=-120 isn't useful, but
y=50 works fine, making x=120
You might have also saved yourself some work by recalling that one of the standard integer-sided right triangles is 5-12-13, and seeing that 50-120-130 would fit your conditions.
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