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

 Jul 20, 2019
 #1
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We can find the length of the missing sides using the information that the area is 240 sq units.  smiley

 

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? smiley

 Jul 20, 2019

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