Exercise 2 Page 148

Let's create an algebraic expression that describes the area of each of the rectangles. Then we can set them equal to one another to solve for x.

Rectangle 1

We will begin with taking a look at the first figure.

To find the area of this rectangle, which we will call A_1, we multiply the given expressions for the side lengths.

Rectangle 2

Again, we will take a look at the second figure.

Similarly, for the second rectangle A_2, we will multiply the expressions for the side lengths to find its area.

Finding the Value of x

Since the figures have the same area, we can set the expressions equal to each other. A_1&= A_2 25x-150 & = 15x By solving the equation, we will determine the value of x that allows this to be true.

When x=15, the rectangles will have the same area. Therefore, answer J is correct.