One leg of a right triangle is 7 feet longer than the other leg. If the hypotenuse of the right triangle measures 13 feet, what is the length of the longer leg?
If one side =x
the other side=x+7, then we have:
13^2=x^2 + (x+7)^2, solve for x
Copyable plaintext:
Solve for x:
169 = x^2+(x+7)^2
169 = x^2+(x+7)^2 is equivalent to x^2+(x+7)^2 = 169:
x^2+(x+7)^2 = 169
Expand out terms of the left hand side:
2 x^2+14 x+49 = 169
Divide both sides by 2:
x^2+7 x+49/2 = 169/2
Subtract 49/2 from both sides:
x^2+7 x = 60
Add 49/4 to both sides:
x^2+7 x+49/4 = 289/4
Write the left hand side as a square:
(x+7/2)^2 = 289/4
Take the square root of both sides:
x+7/2 = 17/2 or x+7/2 = -17/2
Subtract 7/2 from both sides:
x = 5 or x+7/2 = -17/2
Subtract 7/2 from both sides:
Answer: | x = 5 or x = -12(discard)
So, the sides are: 5, 12, 13
