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

Answer 1

Using the formula area=1/2*base*height, solve for height by multiplying both sides by 2 and dividing by base to get height=2*area/base. Plug in the values for base and area to get height=2*240/20=24. You can split the triangle in half making two right triangles that each have a base half the size of the full triangle (20/2=10) and the same height (24). The Pythagorean theorem will give the length of the hypotenuse: a² + b² = c², so 10² + 24² = c², or 100+576=c², so 676=c² or c=sqrt(676)=26. This length, the hypotenuse of the half triangles, is the length of each of the other two sides of the original triangle. The formula for perimeter is s1+s2+s3 (the sum of the side lengths), or [20]+[26]+[26]=72.