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Answer to Question #5673 in Geometry for louise

Question #5673
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
Expert's answer
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.

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