If a right isosceles triangle has an area of 192 cm, what is the height of the triangle?

if the base is 24

Area = (base x height)/2, thus height = 2 (area/base)                

height = 2(192/24)

Which gives you 40

height = 16 cm

the height and half of the base will give you two identical rightangle halves of the triangle

use pythagorean theorem to get the length of the hypotenuse of the 2 identical halves

a^2 + b^2 = c^2

12^2 + 16^2 = c^2

144 + 256 = c^2

(square root)400 = c

20 cm = c

there are 2 of these hypotenuses in the original triangle, so add the base and the 2 "hypotenuses" to get the perimeter

P = 20 + 20 + 24  

P = 64 cm

the perimeter of the isosceles triangle is 64cm

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