SOLUTION: Find the length of the leg of an isosceles triangle whose perimeter is 64 and altitude is 8. P.S: Can you please explain how to solve this when giving the answer? Thanks!

Question 539462: Find the length of the leg of an isosceles triangle whose perimeter is 64 and altitude is 8.

P.S: Can you please explain how to solve this when giving the answer? Thanks!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find the length of the leg of an isosceles triangle whose perimeter is 64 and altitude is 8.
:
Let x = the length of one of the equal sides
then
(64-2x) = the length of the 3rd side
(32-x) = half the length of the 3rd side
:
Two right triangles are formed with the altitude, half the 3rd side and the one leg of the equal side will be the hypotenuse (x)
:
x^2 = 8^2 + (32-x)^2
x^2 = 64 + 1024 - 64x + x^2
x^2 = 1088 - 64x + x^2
x^2 - x^2 + 64x = 1088
64x = 1088
x =
x = 17 is the length of the equal sides
then
64 - 2(17) = 30 is the length of the 3rd side
:
:
Confirm this, find the altitude (a)
a =
a = 8

RELATED QUESTIONS
Find the length of each leg of an isosceles right triangle whose hypotenuse is 12. (answered by ikleyn)

The leg of an isosceles triangle is 6 more than twice the base, if the perimeter is 42cm... (answered by Cromlix)

Find the length of a leg of an isosceles right triangle whose hypotenuse measures 8... (answered by Gogonati)

The length of the base of an isosceles triangle is x. The length of a leg is 2x-5. The... (answered by ewatrrr)

The length of the base of an isosceles triangle is 4x -7. The length of a leg is x. The... (answered by Edwin McCravy)

The perimeter of an isosceles triangle with side lengths s and base length b is given by... (answered by ankor@dixie-net.com)

How do I find the area of an isosceles triangle whose leg lengths are 8, but the base is... (answered by stanbon,jim_thompson5910)

The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of... (answered by ewatrrr)