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)
Solution:
Let x = shorter leg
Therefore, x + 7 = larger leg
Using Pythagorean Theorem:
{{{x^2 + (x+7)^2 = 13^2}}}
{{{x^2 + (x^2 + 14x + 49) = 169}}}
{{{2x^2 + 14x - 120 = 0}}}
Divide both sides by 2
{{{x^2 + 7x - 60 = 0}}}
(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 {{{cm^2}}}