SOLUTION: The hypotenuse of a 45-45-90 triangle measures 14 feet. Part a: Determine the length of a leg of the triangle. Part b: Determine the perimeter of the triangle.

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a 45-45-90 triangle measures 14 feet. Part a: Determine the length of a leg of the triangle. Part b: Determine the perimeter of the triangle.      Log On


   

Question 906605: The hypotenuse of a 45-45-90 triangle measures 14 feet.

Part a: Determine the length of a leg of the triangle.
Part b: Determine the perimeter of the triangle.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's hypotenuse be c
let's legs be a and b
given:
c=14ft
since you have 45-45-90 triangle means legs are same length: a=b
by Pythagorean theorem c%5E2=a%5E2%2Bb%5E2
since a=b and c=14+feet, we have
14%5E2=b%5E2%2Bb%5E2
14%5E2=2b%5E2
14%2A14%2F2=b%5E2
14%2A7=b%5E2
98=b%5E2
sqrt%2898%29=b
sqrt%2849%2A2%29=b

7sqrt%282%29ft=b and 7sqrt%282%29ft=a.........the length of a leg of the triangle
Part b:
the perimeter of the triangle is P=a%2Bb%2Bc
P=7sqrt%282%29ft%2B7sqrt%282%29ft%2B14ft
P=14sqrt%282%29ft%2B14ft
P=14%28sqrt%282%29%2B1%29ft