An isosceles triangle has an area of 150 ft^2. if the base is 12 ft, what is the length of each leg? round the answer to the nearest tenth. 25.0 25.7 27.7 50.4

The area of a triangle is hb/2, we are told the base but not the side lengths. The side length can be found using the pythagorean theorem.

s^2=(b/2)^2+h^2

The height can be found from the area because:

A=bh/2 so 

h=2A/b then our pythagorean identity becomes:

s^2=(b/2)^2+(2A/b)^2

s^2=b^2/4+4A^2/b^2 or a little more neatly

s^2=(b^4+15A^2)/(4b^2), we were told A=150 and b=12 so

s^2=358236/576

s=√(358236/576) ft

s≈24.939 to nearest thousandth (which means that they actually rounded wrong because that's...

s≈24.9 to nearest tenth (they must have made earlier rounding somewhere in the earlier calculations, that's why you use symbols until the final calculation :P)

Anyway, they rounded to 25.0