Question

If in a right-angled triangle ABC, the hypotenuse AB = p, then `overline"AB".overline" AC" + overline"BC".overline" BA" + overline" CA".overline"CB"` is equal to ______ 

Options

• 3p²

• `(3"p"^2)/2`

• p²

• `("p"^2)/2`

Answer 1

If in a right-angled triangle ABC, the hypotenuse AB = p, then `overline"AB".overline" AC" + overline"BC".overline" BA" + overline" CA".overline"CB"` is equal to p².

Explanation:

 

`overline"AB".overline" AC" + overline"BC".overline" BA" + overline" CA".overline"CB"`

= (AB)(AC) cosθ + (BC)(BA) cos(90° - θ) + 0

= AB(ACcosθ + BCsinθ)

= AB`(("AC")^2/"AB" + ("BC")^2/"AB")`

= AC² + BC²

= AB² = p²