an architect is designing a building with a right triangular foot print. the hypotenuse of the triangle is eighty feet longer than one leg of the triangle and forty feet longer than the other leg use the Pythagorean theorem to find the dimensions of the footprint of the building
Accepted Solution
A:
Let the hypotenuse = c One of the legs = c - 80 The other leg = c - 40
(c - 80)^2 + (c - 40)^2 = c^2 Expand the left hand side. c^2 - 160c + 6400 + c^2 - 80c + 1600 = c^2 Subtract c^2 from both sides. c^2 - 160c + 6400 + c^2 - c^2 - 80c + 1600 = 0 Combine like terms. c^2 - 240c + 8000 = 0 (c - 200)(c - 40) is how that factors. It looks like you have two solutions. You don't. Not really (c - 200) = 0 c - 200 = 0 c = 200
The other solution is c - 40 = 0 c = 40
The last solution does not work. Why? It's because the let that was forty smaller than c would give that leg a length of 40 - 40 = 0
So c = 200
The lengths of the triangle are c (the hypotenuse) = 200 The next leg = 200 - 40 = 160 The third leg = 200 - 80 = 120