The perimeter of a right triangle is 50 cm and the hypotenuse is 18cm. find its area.
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bhi phythagirus theorem a^2+b^2=c^2. _(1)
let a,b,c are the sides of given right angle triangle
a+b+c=50
a+b= 50-c
squaring on both sides
a^2+b^2+2ab= 2500 - 100c+c^2
from eq. 1
c^2 + 2ab = 2500- 100c+c^2
2ab= 2500-100c
given that hypotenus is 18 = c
so 2ab = 2500- 18×100
2ab = 700
ab = 350
as se know area or triangle is 1/2 × base× height
1/2 ×b×a
1/2×350
= 125 cm sq.
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