Posted by sydney on Monday, December 19, 2011 at 8:54pm.
A rectangular parcel of land is 70 ft longer than it is wide. Each diagonal between opposite corners is 130 ft. What are the dimensions of the parcel?
The answer is 50 ft by 120 ft, but I don't know how to find the answer

algebra  Steve, Tuesday, December 20, 2011 at 4:29am
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
(y50)(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 integersided right triangles is 51213, and seeing that 50120130 would fit your conditions.
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