Question

A right triangle has hypotenuse p cm and one side q cm .if p-q=1,find the length of the third sides.

Answer 1

Using Pythagoras theorem,
assume third side be x
then, p^2 = q^2 + x^2
x^2 = p^2 - q^2
x^2 = (p+q)(p-q)
x^2 = (p+q)1
x = sqr (p+q).

Answer 2

Answer:

$\sqrt{(p+q)(p-q)}$

Step-by-step explanation:

Given : A right triangle has hypotenuse p cm and one side q cm

To Find :If p-q=1,find the length of the third sides.

Solution :

Hypotenuse = p cm

Base = q cm

Pythagoras theorem : $Hypotenuse^2 = Perpendicular^2+Base^2$

$p^2 = Perpendicular^2+q^2$

$p^2 - q^2= Perpendicular^2$

Identity : $a^2-b^2=(a+b)(a-b)$

$(p+q)(p-q)= Perpendicular^2$

$\sqrt{(p+q)(p-q)}= Perpendicular$

Hence Third side is $\sqrt{(p+q)(p-q)}$