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?

Answer 1

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~ :)

Answer 2

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