SOLUTION: The legs of a right triangle are represented by x and x+2, and the hypotenuse is 10. Find the area of the triangle.

Question 275310: The legs of a right triangle are represented by x and x+2, and the hypotenuse is 10. Find the area of the triangle.
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
The legs of a right triangle are represented by x and x+2, and the hypotenuse is 10. Find the area of the triangle.
By the Pythagorean Theorem we have:
x^2 + (x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x + 4 = 100
x^2 + 2x + 2 = 50
x^2 + 2x - 48 = 0
(x+8)*(x-6) = 0
x+8 = 0 or x-6 = 0 so x = -8 or x = 6. We need x to be positive so x=6.
The two legs of the triangle then are 6 and 6+2 = 8. Since it's a right triangle the legs are the base and the height so the area equals 1/2*(base*height) or 1/2*6*8 = 24.

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