Question

The length of a rectangular floor is 4 feet longer than its width w. The area of the floor is 525 ft^2. A) Write a quadratic equation in terms of w that represents the situation. B) What are the dimensions of the floor? Show your work.​

Answer 1

w² + 4w - 525 = 0

Width of rectangle = 21 feet

Length of rectangle = 25 feet

Explanation:

Given:

Area of rectangular floor = 525 ft²

Find:

Equation

Dimensions of the floor

Computation:

Assume;

Width of rectangle = w feet

So,

Length of rectangle = w + 4 feet

Area of rectangular floor = length x width

Area of rectangular floor = w(w + 4)

525 = w² + 4w

w² + 4w - 525 = 0

w² + (25 - 21)w - 525 = 0

w² + 25w - 21w - 525 = 0

w(w + 25) -21(w + 25)

(w + 25)(w - 21)

So,

w = -25 , w = 21

So,

Width of rectangle = 21 feet

Length of rectangle = w + 4 feet

Length of rectangle = 21 + 4 feet

Length of rectangle = 25 feet