# algebra

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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 -

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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