Question

5. The height of a right-angle triangle is 7 cm less
than its base. If the base is 13 cm. Formulate the
quadratic equation to find the base of the triangle.

Answer 1

Answer:

Let base = x cm and height = (x - 7) cm

Hypotenuse = 13 cm

By Pythagoras theorem,

x2 + (x - 7)2 = 132

x2 + 49 + x2 - 14x = 169

2x2 - 14x - 120 = 0

x2 - 12x + 5x - 60 = 0

x( x - 12) + 5 (x - 12) = 0

(x - 12) (x + 5) = 0

x - 12 = 0 or x + 5 = 0

x=12 or x=-5 (rejecting)

The other two sides are 12 cm and 5 cm.