SOLUTION: If the area of an isosceles triangle is 56 units squared and the base is one third of the height, what is the perimeter? Round all decimals to one decimal place to determine the p

Algebra ->  Rectangles -> SOLUTION: If the area of an isosceles triangle is 56 units squared and the base is one third of the height, what is the perimeter? Round all decimals to one decimal place to determine the p      Log On


   

Question 1051233: If the area of an isosceles triangle is 56 units squared and the base is one third of the height, what is the perimeter? Round all decimals to one decimal place to determine the proper solution
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29bh=56
%28h%2F3%29h=112
h%5E2=336
h=sqrt%28336%29
b=sqrt%28336%29%2F3
The height and half the base form a right triangle.
The side of the isosceles triangle is the hypotenuse of that triangle.
h%5E2%2Bb%5E2=s%5E2
%28sqrt%28336%29%29%5E2%2B%28sqrt%28336%29%2F6%29%5E2=s%5E2
336%2B336%2F36=s%5E2
s%5E2=%2837%2F36%29%28336%29
s=%282%2F3%29sqrt%28777%29
So then,
P=s%2Bs%2Bb
P=%284%2F3%29sqrt%28777%29%2Bsqrt%28336%29%2F3