Question

Cynthia Besch wants to buy a rug for a room that is 20 ft wide and 35 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 594 sq ft of carpeting. What dimensions should the rug have?

Answer 1

Answer:

18ft wide and 33 ft long

Step-by-step explanation:

We are told in the question that:

Cynthia Besch wants to buy a rug for a room that is 20 ft wide and 35 ft long.

The Area of the carpeting she must have = 594 ft²

To solve for this, we have:

Length × Width = Area of a rectangle

594ft² = Length × Width

594ft² = (20 - x) (35 - x)

594 = 700 - 20x - 35x + x²

594 = 700 - 55x + x²

Collect like terms

x² - 55x + 700 - 594

x² - 55x + 106

We factorise

x² - 2x - 53x + 106

(x² - 2x) -(53x + 106)

x(x - 2) -53(x - 2)

(x - 2)(x - 53)

x - 2 = 0, x = 2

x - 53 = 0, x = 53

We choose the least value for x

Hence, x = 2

Length = 20 - 2 = 18ft

Width = 35 - 2 = 33ft

The dimensions the rug should have is 18ft by 33ft, meaning 18ft wide and 33 ft long