SOLUTION: Find the area of a triangle whose sides measure, 13 feet, 13 feet, and 10 feet.

Question 292763: Find the area of a triangle whose sides measure, 13 feet, 13 feet, and 10 feet.
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
This is an isosceles triangle with same sides 13 and base 10. If we drop an altitude to the base from the vertex between the two equal sides we create two right triangles with hypotenuse 13 and one leg 10/2 = 5.
By the Pythagorean Theorem then, if the altitude is a we have:
13^2 = 5^ + a^2
a^2 = 169 - 25
a^2 = 144
a = 12
The area of the original triangle then is (base*altitude)/2 or:
(10*12)/2 = 120/2 = 60
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