Question

Natoshia's den is 4 feet longer than it is wide. If the​ den's area is 320 square​ feet, what are the dimensions of the​ room?

Answer 1

width = 16 ft

length = 20 ft

Explanation:

Let width = x

If the length is 4 ft longer than the width, then

⇒ length = x + 4

Area of a rectangle = width × length

Given:

• area = 320
• width = x
• length = x + 4

Substituting these values into the equation for the area of a rectangle and solving for x:

⇒ 320 = x(x + 4)

⇒ 320 = x² + 4x

⇒ x² + 4x - 320 = 0

⇒ (x - 16)(x + 20) = 0

⇒ x = 16, -20

As distance is positive, then x = 16 only.

Therefore, width = 16 ft and length = 20 ft

Answer 2

Dimensions : 16 x 20

• Let the width be x

• then the length: x + 4

area of rectangle = Length * Width

solving steps:

• (x+4)(x) = 320

• x² + 4x = 320

• x² + 4x - 320 = 0

• x² +20x -16x -320 = 0

• x(x + 20) -16(x+20) = 0

• (x-16)(x+20) = 0

• x = 16, -20

• x = 16 [ As length or width can never be negative ]

So we found Width = 16 feet

Length:

• 16 + 4

• 20 feet