SOLUTION: The perimeter of an isosceles triangular lot is 210 m. If each congruent side is 2/3 the third side, what are the lengths of the sides. Find the area of the triangle.

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Question 155021: The perimeter of an isosceles triangular lot is 210 m. If each congruent side is 2/3 the third side, what are the lengths of the sides. Find the area of the triangle.
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
Let known that sideA=A & sideB=B are congruent and the 3rd side=sideC=C
So,
A=%282%2F3%29C
B=%282%2F3%29C
C=C
Perimeter=A%2BB%2BC, or since A=B -- congruent, then P=2A%2BC
210m=%282%2F3%29C%2B%282%2F3%29C%2BC
210=%284%2F3%29C%2BC
210=%284C%2B3C%29%2F3
630=7C ---> cross%28630%2990%2Fcross%287%29=cross%287%29C%2Fcross%287%29
C=90meters ------------------------> side C
A=B=%282%2F3%2990=180%2F3=60meters --------> side A & side B
Area=%281%2F2%29bh
Remember: base=sideC=90
Solve h by Pyth theorem:
B%5E2=h%5E2%2B%28C%2F2%29%5E2 -----. we use only 1%2F2 of side C for a right triangle to use Pyth theorem:
h=sqrt%28B%5E2-%28C%2F2%29%5E2%29
h=sqrt%2860%5E2-%2890%2F2%29%5E2%29
h=sqrt%283600-2025%29=sqrt%281575%29=39.7%3E=40m
Then, A=%281%2F2%2990%2A40=1800m%5E2
thank you,
Jojo