Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
a. 8 in.
b. 11.3 in.
c. 8.5 in.
d. 6.2 in.

Option C. 8.5 in.

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The formula of area of triangle is equal to

In this problem

we have

substitute

------> equation 1

Remember that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  

a,b,c be the lengths of the sides of a triangle.  

The area is given by:

where

p is half the perimeter

p=

we have

Find the half perimeter p

p=

Find the area

Substitute the value of the area in the equation 1 and solve for x

step-by-step explanation: given equation a = h(b 1+b 2)

also we are given values of a, h and b 1 as :

a = 16, h = 4, and b 1 = 3.

in order to solve it for b 2, we need to plug the given values of   a, h and b 1 .

therefore, plugging values of   a, h and b 1   in given equation, we get

16 = 4( 3 + b 2)

first dividing both sides by 4, we get

4 = 3 + b 2

subtracting 3 from both sides, we get

4 -3 = 3 -3 + b 2

1 = b 2.