Find the perimeter of an isosceles triangle with base length 20 and area 240.

Guest Jul 20, 2019

#1**+5 **

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,

10^{2} + 24^{2} = c^{2}

100 + 576 = c^{2}

676 = c^{2}

c = √676

c = 26

Now do you see how to finish it?

hectictar Jul 20, 2019