Question

The length of a rectangle exceeds its width by 5

inches, and the area is 14 square inches. What
are the length and width of the rectangle?
Separate the answers with a comma.

Answer 1

length = 7 inch

width = 2 inch

Explanation:

Let the width be "w".

Given:

Length = W + 5

Area = 14 in²

• We know that the formula for the area of a rectangle:

Area = width × length

• Substituting the given information into the formula, we have:

(W + 5) × W = 14

Expand the equation

W² + 5W = 14

Rearrange the equation

W² + 5W - 14 = 0

• Now, we can solve this quadratic equation directly.

Factoring or using the quadratic formula, we find:

W = 2 or W = -7

Since the width cannot be negative, we take Width = 2 as the valid solution.

• Plugging this value back into the equation for the length:

Length = W+ 5 = 2 + 5 = 7

Therefore, the length and width of the rectangle are 7 inches and 2 inches, respectively.

Answer 2

• 2 in and 7 in

-------------------------------

Let the length be l and width be w.

We are given that:

• 1) l = w + 5
• 2) lw = 14 (area is the product of length and width)

Substitute w + 5 for l into second equation:

• w(w + 5) = 14
• w² + 5w = 14
• w² + 5w - 14 = 0
• w² + 7w - 2w - 14 = 0
• w(w + 7) - 2(w + 7) = 0
• (w + 7)(w - 2) = 0
• w = - 7 or w = 2

The first root is discarded as negative.

So the width is 2 in, then the length is:

• l = 2 + 5
• l = 7 in