SOLUTION: The lengths of two sides of an isosceles triangle are 10 cm and 12 cm. Find the number of square centimeters in the positive difference between the greatest and least possible area

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Question 1103130: The lengths of two sides of an isosceles triangle are 10 cm and 12 cm. Find the number of square centimeters in the positive difference between the greatest and least possible areas for this triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If 10 is the base and 12 is the congruent side,
12%5E2=X%5E2%2B%2810%2F2%29%5E2
X%5E2=144-25
X=sqrt%28119%29
and
A%5B1%5D=%281%2F2%29%2810%2F2%29%28sqrt%28119%29%29
A%5B1%5D=%285%2F2%29sqrt%28119%29
If 12 is the base and 10 is the congruent side,
10%5E2=X%5E2%2B%2812%2F2%29%5E2
X%5E2=100-49
X=sqrt%2851%29
and
A%5B2%5D=%281%2F2%29%2812%2F2%29%28sqrt%2851%29%29
A%5B2%5D=3sqrt%2851%29
.
.
So,
dA=A%5B1%5D-A%5B2%5D
dA=%285%2F2%29sqrt%28119%29-3sqrt%2851%29