Question

Marcello is replacing a rectangular sliding glass door with dimensions of (x + 7) and (x + 3) feet. The area of the glass door is 45 square feet. What are the length and width of the door? Complete the explanation of how you got your answer.

I found the area of the glass door by multiplying the length by the width, which is _____. I set this product, which represents the area in terms of x equal to ____ . Then, I rewrote the equation so one side was 0 and solved for x and got x=____. A dimension of the door can't be negative so x = ____ .

Answer 1

To find the length and width of the rectangular sliding glass door, we can solve the equation for the area and find the positive solution for x. The width of the door is (x + 3) = 16 feet, and the length of the door is (x + 7) = 20 feet.

Step-by-step explanation:

To find the length and width of the rectangular sliding glass door, we need to solve the equation for the area. The area of a rectangle can be found by multiplying the length by the width. So we have:

(x + 7) * (x + 3) = 45

Simplifying the equation:

x² + 10x + 21 = 45

Setting the equation equal to 0:

x² + 10x + 21 - 45 = 0

x² + 10x - 24 = 0

Factoring the quadratic equation or using the quadratic formula will give us two solutions for x. However, since a dimension of the door cannot be negative, we can ignore the negative solution.

Therefore, the width of the door is (x + 3) = (13 + 3) = 16 feet, and the length of the door is (x + 7) = (13 + 7) = 20 feet.