SOLUTION: If the perimeter of an isosceles triangle is 36 cm and if the altitude to its base is 12 cm, what is the triangle's area?

Algebra ->  Triangles -> SOLUTION: If the perimeter of an isosceles triangle is 36 cm and if the altitude to its base is 12 cm, what is the triangle's area?      Log On


   

Question 432766: If the perimeter of an isosceles triangle is 36 cm and if the altitude to its base is 12 cm, what is the triangle's area?
Found 2 solutions by checkley79, Gogonati:
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
A=bh/2
b=12/2=6 cm.
6^2+h^2=12^2
36+h^2=144
h^2=144-36
h^2=108
h=sqrt108
h=10.4 ans. for the height.
A=6*10.4/2
A=62.4/2=31.2 cm ^2 is the AREA.

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let's x cm the base of isosceles triangle, Since its perimeter is 36cm, one from the equal sides will be:
%2836-x%29%2F2cm If we draw the altitude on the base, this altitude bisect the
base. Applying the Pythagorean theorem we can find the base.
%2836-x%29%5E2%2F4-x%5E2%2F4=12%5E2,solve the equation,
%281296-72x%2Bx%5E2-x%5E2%29%2F4=144,multiply by 4 and simplify the equation,
-72x=-720
x=10. As you know the area of triangle is given by the formula:
A=%281%2F2%29%2A%28b%2Ah%29, substitute h=12 cm and b=10 cm
A=%281%2F2%29%2A%2810%2A12%29=60cm%5E2
The area of triangle is 60 cm^2.