Question

A rectangular Persian carpet has an area of (x² + 8x − 20) ft2 and a length of (x + 10) feet. The Persian carpet is displayed on a wall. The wall has a width of (x + 2) feet and an area of (x² + 17x + 30) feet. Find the dimensions of the rug and the wall if x = 20 feet.

Answer 1

To find the dimensions of the rug and the wall, substitute x = 20 feet into the given expressions for the area and length of the carpet and the width and area of the wall.

Step-by-step explanation:

To find the dimensions of the rug and the wall, we need to substitute x = 20 feet into the given expressions for the area and length of the carpet and the width and area of the wall. Let's start with the carpet:

Area of carpet = x² + 8x - 20 = (20)² + 8(20) - 20 = 400 + 160 - 20 = 540 ft²

Length of carpet = x + 10 = 20 + 10 = 30 feet

Next, let's find the dimensions of the wall:

Area of wall = x² + 17x + 30 = (20)² + 17(20) + 30 = 400 + 340 + 30 = 770 ft²

Width of wall = x + 2 = 20 + 2 = 22 feet