A portion of a rectangle is shaded as shown. The area of the shaded region is 78 in.2. What is the value of x? Show your work.

Solution:

Finding the area of the large rectangle.

We know that:

This means that we got two ways to find the area of the triangle.

Those methods are:

Let's put these two methods in an equation as both are equal.

Substituting the base of the triangle:

Simplifying the RHS:

Simplifying the LHS:

Dividing 6 both sides:

Since the height is 3 in, the measure of x is 5 in because the sum of the height and x must be 8.

idk

step-by-step explanation: