Question

Tricia is building the framework for an entryway window for a house under construction. The window is in the shape of a rectangle. The height of the window is represented by the expression 6x – 7 feet. To allow for the maximum amount of light in the entryway, the area of the window is represented by the expression 24x – 28 square feet. What is the base of the window in feet

Answer 1

The base of the window will be 4 feet.

Explanation

Suppose, the base of the window is  $y$ feet.

The window is in the shape of a rectangle and the height of the window is $(6x-7)$ feet.

So, the area of the window will be:  $base*height = y(6x-7)$ feet²

Given that, the area of the window is represented by the expression $(24x-28)$ feet²

So, the equation will be ......

$y(6x-7)= 24x-28\\ \\ y=\frac{24x-28}{6x-7}=\frac{4(6x-7)}{6x-7} =4$

Thus, the base of the window will be 4 feet.