An isosceles triangle has an area of 125 ft². If the base is 14 ft, what is the length of each leg? Round the answer to the nearest tenth. (Hint: Use the formula for the area of a triangle to solve for the height. Then with half of the base and the height you just solved for, find the hypotenuse.)
To find the height of the triangle, we can use the formula for the area of a triangle:
Area = 1/2(base)(height)
125 = 1/2(14)(height)
125 = 7(height)
height = 125/7
height ≈ 17.857 ft
Now that we have the height, we can use it to find the length of each leg. The legs are the same length, so we can divide the base in half to find the length of one leg:
Leg = √(height² + (base/2)²)
Leg = √(17.857² + (14/2)²)
Leg = √(318.745 + 49)
Leg = √367.745
Leg ≈ 19.2 ft
Therefore, the length of each leg of the isosceles triangle is approximately 19.2 ft.