BAC=90 degrees. The length of the three sides are x cm, (x+7) cm, and (x+8) cm.

Question

a. Write down and simplify a quadratic equation in x which links the three sides of the triangle.
b. Solve the quadratic equation found in (a)
c. Write the value of the perimeter of the triangle.

Answer 1

a. x^2 + (x + 7)^2 = (x + 8)^2 ... 2 x^2 + 14 x + 49 = x^2 + 16 x + 64

b. x^2 - 2x - 15 = 0 ... (x - 5) (x + 3) = 0 ... x = 5 , x = -3
... the negative result is not realistic

c. a 5-12-13 Pythagorean triple ... perimeter = 30