Question

John is placing cement tiles for a patio in a rectangle surrounding a

rectangular fire pit. The fire pit has a width of x ft and a length that is 4
times the width. The entire patio is 9 ft wider and 13 ft longer than the fire
pit. What is the area that he will need to buy tiles for?

Answer 1

31x + 55 sq. ft.

Explanation:

Width of Fire Pit = x ft. Length of Fire Pit = 4x ft.

Width of Patio = x + 5 ft. Length of Patio = 4x + 11 ft. Area of Fire pit = 4x * x = 4x² sq, ft.

Total Area of Rectangular Patio (including Fire pit) = (4x + 11)(x+5)

= 4x² + 31x + 55 sq. ft.

Area for which tiling is done = Area of Rectangular patio - Area of fire pit

= 4x² + 31x + 55 - 4x²

= 31x + 55 sq. ft.