The sum of the lengths of the three sides of a right triangle is 18. The sum of the squares of the lengths of the three sides is 128. What is the area of this right triangle?

Source: mathcontest.olemiss.edu 3/5/2012

**SOLUTION
**

By the Pythagorean theorem

Substitute the value of into Eq. (2)

Substitute the value of into Eq. (1)

Substitute the value of

Divide both sides by 4

Area of right triangle =

**Answer**: .

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