Hypotenuse of right triange is 5ft long. The longer leg is 1 ft longer than the shorter one. Find the side lenghts of the triangle?
Solve for x:
x^2+(x+1)^2 = 25
Expand out terms of the left hand side:
2 x^2+2 x+1 = 25
Divide both sides by 2:
x^2+x+1/2 = 25/2
Subtract 1/2 from both sides:
x^2+x = 12
Add 1/4 to both sides:
x^2+x+1/4 = 49/4
Write the left hand side as a square:
(x+1/2)^2 = 49/4
Take the square root of both sides:
x+1/2 = 7/2 or x+1/2 = -7/2
Subtract 1/2 from both sides:
x = 3 or x+1/2 = -7/2
Subtract 1/2 from both sides:
Answer: |x = 3 The shorter leg. 3+1=4 The longer leg. Hypotenuse=5
