SOLUTION: A landscape architect is making a path between two trees, A and B, that are 60 feet apart. He wants the path to be 70 feet long and to contain one right angle, as shown. Write an e

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A landscape architect is making a path between two trees, A and B, that are 60 feet apart. He wants the path to be 70 feet long and to contain one right angle, as shown. Write an e      Log On

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Question 1064331: A landscape architect is making a path between two trees, A and B, that are 60 feet apart. He wants the path to be 70 feet long and to contain one right angle, as shown. Write an equation to determine how long the legs of the path should be. Find the lengths to the nearest tenth of a foot. (Note: will need to solve using the quadratic formula)
I tried to solve using x^2 +(70-x)^2 = 60^2 and ended up with one side as 9.3 and the other as 60.7 but I am confused because I did not have to use the quadratic formula.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Just one right angle opposite of the 60 foot distance between the two trees; being hypotenuse of a right triangle, same as half of a rectangle. Path length wanted, 70 feet.


Let x be one of the leg lengths. The other leg length is 70-x.
Your equation is correct.
x%5E2%2B%2870-x%29%5E2=60%5E2
Simplify and solve.

x%5E2%2B70%5E2-140x%2Bx%5E2=3600

2x%5E2-140x%2B70%5E2-3600=0

2x%5E2-140x%2B4900-3600=0

x%5E2-70x%2B650=0
Can the quadratic be factored?
No.
Discriminant 4900-4%2A650=2300=10%5E2%2A23

General Solution Formula for a Quadratic Equation.....
x=%2870%2B-+10%2Asqrt%2823%29%29%2F%282%2A2%29
x=%2835%2B-+5%2Asqrt%2823%29%29%2F2

x=5.510 or x=29.490
You can check if these work in the original x%5E2%2B%2870-x%29%5E2=60%5E2 equation or not.