Answer to Question #5673 in Geometry for louise

Question

the perimeter of a right triangle is 24cm. one leg is 2cm longer than the other leg and 2cm shorter than the hypotenuse. find the area of the right triangle

Answer 1

Let's construct the system of equations (a and b are legs and c is the hypotenuse):

a+b+c = 24
a+2 = b
a-2 = c

Solving it:

a+(a+2)+(a-2) = 24
3a = 24
a = 8
b = 10

Here we got both legs of the triangle. So, the area of the triangle is

S = a*b/2 = 8*10/2 = 40 cm^2.