Use the equation from the exercise to evaluate the square root to find the area of the triangle. How can we use the area of a triangle to find its height?
8 centimeters
Practice makes perfect
We want to find the height of a triangle, given its side lengths and a formula for its area. Let's take a look at the given figure.
From the exercise, we know that the area of this triangle is represented by the following formula.
A=sqrt(s(s-21)(s-17)(s-10))
In this formula, A is the area of the triangle and s is half of the perimeter of the triangle. Let's calculate the value of s.
s=17+21+10/2 ⇒ s= 24
Notice that height is not included in the given formula. However, we do know another formula for the area of a triangle that does include the height of the triangle.
A=1/2bh
In this equation, A is the area of a triangle, b is the base length, and h is the height of a triangle. Looking at the given figure, we can see that the base length is 21 centimeters. Both of these equations equal the area of the triangle, so let's set them equal to each other and solve the equation for h.
