SOLUTION: A piece of metal has the shape of a right triangle. The hypotenuse is 3 ft shorter than four times the shortest side and the longer side is 10 ft longer than twice the shorter side

Question 1077439: A piece of metal has the shape of a right triangle. The hypotenuse is 3 ft shorter than four times the shortest side and the longer side is 10 ft longer than twice the shorter side. What is the length of the hypotenuse of the triangle?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
shorter side=x
longer side is 2x+10
hypotenuse is 4x-3
square them all
x^2+(2x+10)^=(4x-3)^2. Note, binomial expansion (a+b)^2=a^2+2 ab (the internal products are doubled)+b^2
x^4x^2+40x+100=16x^2-24x+9
5x^2+40x+100=16x^2-24x+9
0=11x^2-64x-91
x=(1/22)(64+/- sqrt (4096+4004); sqrt 8100=90
x=(1/22)(64+/-90), use only the + root.
x=(1/22)154=7
sides are 7, 24, with hypotenuse 25, a well known right triangle.
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