Answer:
Therefore Area of triangle RHP is 60 unit².
Step-by-step 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
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the values we get
[tex](RP)^{2}= (RH)^{2}+(HP)^{2}\\\\17^{2}-15^{2}= (RH)^{2}\\\\(RH)^{2}=64\\Square\ Rooting\ we\ get\\RH =\pm \sqrt{64} \\\therefore RP = 8\ unit\\[/tex]
Now Area of triangle is given as
[tex](\textrm{Area of triangle}=\dfrac{1}{2}\times Base\times Height[/tex]
Substituting the values we get
[tex](\textrm{Area of triangle RHP}=\dfrac{1}{2}\times HP\times RH[/tex]
[tex](\textrm{Area of triangle RHP}=\dfrac{1}{2}\times 15\times 8=60\ unit^{2}[/tex]
Therefore Area of triangle RHP is 60 unit².
