SOLUTION: The hypotenuse of a right triangle is 13cm. One of the legs is 7cm longer than the other leg. Find the area of the Triangle (Please explain how you got your answer)

Question 971099: The hypotenuse of a right triangle is 13cm. One of the legs is 7cm longer than the other leg. Find the area of the Triangle (Please explain how you got your answer)
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right triangle is 13cm. One of the legs is 7cm longer than the other leg. Find the area of the Triangle (Please explain how you got your answer)
Solution:
Let x = shorter leg
Therefore, x + 7 = larger leg
Using Pythagorean Theorem:

Divide both sides by 2

(x - 5)(x + 12) = 0
x - 5 = 0 or x + 12 = 0
x = 5 [Disregard the negative root]
The larger leg is equal to x + 7 = 12
The area is equal to (1/2)(5)(12) = 30
Answer: 30
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