An isosceles triangle has an area of 125 feet. if the base is 14 feet, what is the length of each leg

Area of a right triangle is (1/2) x base x height
Cut the isosceles triangle in half to create a 90° triangle.
Then, (1/2)Area = (1/2) base x height
           (1/2)(125) = (1/2) (14/2) x height
                    125  =             7     x    h
                  125/7  =  h

Now use Pythagorean Theorem to find the hypotenuse (c):
a² + b² = c²
(7)² + (125/7)² = c²
49 +  318.88  = c²
    367.88       = c²
     19.18        = c
Since it is an isosceles triangle, the legs are the same length.

the length of each leg is ≈ 19.18

Look at the picture.
The formula of the area of a triangle is:

substitute:


Use the Pythagorean theorem