A right triangle has perimeter 20. If the sum of the squares of the triangle's three sides is 162,
what is the area of the triangle?
what is the area of the triangle?
A right triangle has perimeter 20. If the sum of the squares of the triangle's three sides is 162,
what is the area of the triangle?
Let the three sides are a, b and c......think a and b are sides and c as the hypotenuse of the right angle traingle.
a+b+c = 20 , a^2+b^2+c^2 = 162
from phythogoreous theorem , a^2+b^2 = c^2
use below formula
(a+b+c) ^2 = a^2+b^2+c^2+2ab+2bc+2ca
20 ^ 2 = 162 + 2ab+2bc+2ca
ab+bc+ca = 400 - 162/2 = 119
since a^2+b^2 = c^2 and a^2+b^2+c^2 = 162 => 2 * c^2 = 162 => c^2 = 81 => c = 9
ab+bc+ca = 119 => ab+9b+9a (substitute the value of c from above)
ab+9(a+b) = 119
ab+9(11) = 119 ( since, a+b+c = 20 and c= 9 => a+b =11)
=> ab = 119 -99 = 20
=> ab = 20
area of triangle = 1/2* a * b = 1/2 * 20 = 10
Therefor area of triangle is 10
