Question

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

Answer 1

Look at the picture.
The formula of the area of a triangle is:
`A_\Delta=(1)/(2)bh`

`b=14\ ft.;\ A_\Delta=125\ ft.`
substitute:

`(1)/(2)\cdot14\cdot h=125\\\\7h=125\ \ \ |:7\\\\h=(125)/(7)\ ft.`

Use the Pythagorean theorem

`l^2=\left((14)/(2)\right)^2+\left((125)/(7)\right)^2\\\\l^2=7^2+(15625)/(49)\\\\l^2=49+(15625)/(49)\\\\l^2=(2401)/(49)+(15625)/(49)\\\\l^2=(18026)/(49)\\\\l=\sqrt{(18026)/(49)}\\\\l=(√(18026))/(7)\approx19.18\ ft.`

Answer 2

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.

Answer: the length of each leg is ≈ 19.18