Question

Joan wants to determine the longest side of a four-sided yard where she wants to build a house. A diagonal connecting two opposite vertices of the site is 150 feet in length while the other diagonal has a different length. The area of the yard is 7500 sq.ft. What is the length of the longest side?

Answer 1

We know the area is length * width = 7500

Assuming we've got a rectangular yard, that diagonal is the hypotenuse of a right triangle with sides length and width. By Pythagoras, that means

length^2 + width^2 = diagonal^2 = 150*150 = 22500

Now we can use substitution to solve for the values of length and width.

length = 7500/width

Let's make the notation a bit neater and use L and W instead

plugging that into the second equation, we get

(7500/W)^2 + W^2 = 22500

Now solve that for W (positive values only), and use W to find L. Compare the two and choose the longer side.