Question

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Answer 1

Using Pythagoras Theorem

`"(hypotenuse)"^2 = sqrt("(height)"^2 + "(base)"^2)`

`AC^2 = sqrt(AB^2 + BC^2)`

`(13)^2 =sqrt( (x )^2 + (x - 7)^2)`

169 = x² + (x - 7)²

169 = x² + x² - 14x + 49

2x² - 14x - 120 = 0

x² - 7x - 60 = 0

x² - 12x + 5x - 60 = 0

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

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

Either x - 12 = 0 or x + 5 = 0

x = 12 or x = - 5

Since

Base of right angled triangle = x cm = 12 cm

Right triangle height = x – 7 cm

= 12 - 7

= 5 cm