Find the perimeter of an isosceles triangle with base length 20 and area 240.
We can find the length of the missing sides using the information that the area is 240 sq units.
area of triangle = ( 1/2 )( base )( height ) Plug in the information we're given.
240 = ( 1/2 )( 20 )( height ) Multiply 1/2 by 20
240 = ( 10 )( height ) Divide both sides of the equation by 10
24 = height
So we know the base is 20 and the height is 24
When we draw a height to the base, we split the triangle into two smaller congruent triangles.
(We can know they're congruent by the hypotenuse-leg congruence theorem.)
And so the height splits the base exactly in half.
That means the length of the missing leg in each of the right triangles = 20/2 = 10
So by the Pythagorean Theorem,
102 + 242 = c2
100 + 576 = c2
676 = c2
c = √676
c = 26
Now do you see how to finish it?