Question

A rectangular rug has an area of 70 square feet, and its width is exactly 3 feet longer than its length. What is the length, in feet, of the rug?

a) 7
b) 10
c) 5
d) 8

Answer 1

To find the length of a rectangular rug with an area of 70 square feet and a width that is 3 feet longer than its length, we set up and solve a quadratic equation. The length of the rug is 7 feet.

Step-by-step explanation:

The question asks for the length of a rectangular rug that has an area of 70 square feet and a width that is 3 feet longer than the length. Let's represent the length of the rug as x feet. Then, the width will be x + 3 feet. The area of a rectangle can be found using the formula Area = length × width. So in this case, the area is x × (x + 3) square feet. We know the area is 70 square feet, so:

x(x + 3) = 70

Solving this equation will give us the length x:

1. 
   
3. x² + 3x = 70
4. 
   
6. x² + 3x - 70 = 0
7. 
   
9. Factor the quadratic equation: (x + 10)(x - 7) = 0
10. 
    
12. Solve for x: x = -10 or x = 7

Since a length can't be negative, the length of the rug must be 7 feet, which is answer choice (a).