A right triangle has hypotenuse of length p cm

Asked by admin @ 23/08/2021 in Math viewed by 708 People

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

Answered by admin @ 23/08/2021

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

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