math
posted by gaurav on .
2. One side of a right triangle is 12.5 ft. The perimeter is 38.7 ft. What is the length of the hypotenuse and the other unknown side?

let x = hypotenuse
let y = the length of the other leg
we have two equations, two unknowns here.
recall that perimeter of a triangle is just,
P = a + b + c
substituting,
38.7 = x + y + 12.5
x + y = 38.7  12.5
x + y = 26.2
x = 26.2  y : : equation (1)
recall that for any right triangle, we can solve for hypotenuse using the Pythagorean theorem:
c^2 = a^2 + b^2
substituting,
y^2 = x^2 + 12.5^2
y^2 = x^2 + 156.25 : equation (2)
now, we substitute eqn (1) to eqn (2):
y^2 = (26.2  y)^2 + 156.25
y^2 = 686.44  52.4y + y^2 + 156.25
y^2  y^2 + 52.4y = 842.69
52.4y = 842.69
y = 16.08 ft (hypotenuse)
x = 26.2  y = 10.12 ft (other leg)
hope this helps~ :) 
P = Perimeter
a = First side = 12.5 ft
b = Second side
c = Hypotenuse
c = sqrt ( a ^ 2 + b ^ 2 )
c = sqrt ( 156.25 + b ^ 2 )
P = a + b + c = 38.7
12.5 + b + sqrt ( 156.25 + b ^ 2 ) = 38.7
b + sqrt ( 156.25 + b ^ 2 ) = 38.7 12.5
b + sqrt ( 156.25 + b ^ 2 ) = 26.2
sqrt ( 156.25 + b ^ 2 ) = 26.2  b Square both sides
156.25 + b ^ 2 = ( 26.2  b ) ^ 2
156.25 + b ^ 2 = 26.2 ^ 2  2 * 26.2 * b + b ^ 2
156.25 + b ^ 2 = 686.44  52.4 b + b ^ 2
b ^ 2 + 52.4 b  b ^ 2 = 686.44  156.25
52.4 b = 530.19 Divide both sides with 52.4
b = 530.19 / 52.4
b = 10.118129771 ft
c = sqrt ( a ^ 2 + b ^ 2 )
c = sqrt ( 12.5 ^ 2 + 10.118129771
^ 2 )
c = sqrt ( 156.25 + 102.37655 )
c = sqrt ( 258.62655 )
c = 16.08187 ft