SOLUTION: 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?

Question 169031: 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?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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?
.
Let w = width
then
w+70 = length
.
Applying Pythagorean theorem:
w^2 + (w+70)^2 = 130^2
w^2 + w^2+70w+70w+4900 = 16900
2w^2 + 140w + 4900 = 16900
w^2 + 70w + 2450 = 8450
w^2 + 70w - 6000 = 0
.
Factoring the left:
(w-50)(w+120) = 0
.
w = {-120, 50}
.
toss out the negative solution:
width is 50 feet
length is 50+70= 120 feet

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