Question

How to determine the area of RHP?

Answer 1

Therefore Area of triangle RHP is 60 unit².

Explanation:

Given:

RH ⊥ HP

HP = 15 = Longer leg

RP = 17 = Hypotenuse

RH = Shorter leg

To Find:

Area of Δ RHP = ?

Solution:

In Right Angle Triangle RHP By Pythagoras theorem we have

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

Substituting the values we get

`(RP)^(2)= (RH)^(2)+(HP)^(2)\\\\17^(2)-15^(2)= (RH)^(2)\\\\(RH)^(2)=64\\Square\ Rooting\ we\ get\\RH =\pm √(64) \\\therefore RP = 8\ unit\\`

Now Area of triangle is given as

`(\textrm{Area of triangle}=(1)/(2)* Base* Height`

Substituting the values we get

`(\textrm{Area of triangle RHP}=(1)/(2)* HP* RH`

`(\textrm{Area of triangle RHP}=(1)/(2)* 15* 8=60\ unit^(2)`

Therefore Area of triangle RHP is 60 unit².