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 pr

Algebra ->  Triangles -> 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 pr      Log On


   

Question 888499: 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.
The choices are:
1) 76.7 units
2) 30.5 units
3) 43.3 units
4) 69.2 units
5) 54.8 units
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=%281%2F2%29bh=%281%2F2%29%28%281%2F3%29h%29h=56
h%5E2=336
h=sqrt%28336%29=4sqrt%2821%29
b=%281%2F3%29%284sqrt%2821%29%29=%284%2F3%29sqrt%2821%29
The other side is the hypotenuse of a right triangle formed by (1/2) the base and the height. Use the Pythagorean theorem.
S%5E2=%28b%2F2%29%5E2%2Bh%5E2
S%5E2=%28%282%2F3%29sqrt%2821%29%29%5E2%2B336
S%5E2=%284%2F9%2921%2B336
S%5E2=84%2F9%2B3024%2F9
S%5E2=3108%2F9
S=sqrt%283108%29%2F3=%282%2F3%29sqrt%28777%29
Then,
P=2S%2Bb
P=%284%2F3%29sqrt%28777%29%2B%284%2F3%29sqrt%2821%29
P=%284%2F3%29%28sqrt%28777%29%2Bsqrt%2821%29%29