SOLUTION: The area of an isosceles triangle is 36 square inches. The ratio of the lenght of the base to its height is 2:1. What is the perimeter of the triangle? Thank you so much !

Algebra ->  Triangles -> SOLUTION: The area of an isosceles triangle is 36 square inches. The ratio of the lenght of the base to its height is 2:1. What is the perimeter of the triangle? Thank you so much !      Log On


   

Question 865266: The area of an isosceles triangle is 36 square inches. The ratio of the lenght of the base to its height is 2:1. What is the perimeter of the triangle? Thank you so much !
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A picture will help show that, if base is x, then altitude is x/2.
Area, highlight_green%2836=%281%2F2%29%28base%29%28altitude%29%29
%281%2F2%29x%28x%2F2%29=36
%28x%5E2%2F4%29=36
x=12 and altitude is x%2F2=6
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The triangle is TWO right triangles, each leg is 6 inches.
Hypotenuse is the length of each of the two equal sides of the ISOSCELES triangle.
%28hypotenuse%29%5E2=6%5E2%2B6%5E2
hypotenuse=sqrt%2872%29 or sqrt%282%2A36%29=6sqrt%282%29
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Perimeter of the isosceles triangle is 2%2A6sqrt%282%29%2B12
perimeter is highlight%2812sqrt%282%29%2B12%29