Question

The length of a rectangle exceeds its width by 5 inches. The

area of the rectangle is 84 square inches. Find its dimensions.

Answer 1

The area is the product of length and width, which is to say that the length and width are factors of the area.

Assuming the dimensions are integers, you want factors of 84 that differ by 5.

Explanation:

... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12

The last of these pairs differ by 5, so ...

the length is 12 inches

the width is 7 inches.

The answer is l=12, w=7

Answer 2

Explanation:

Givens

Let the width be w

Let the length be w + 5

Let the area = 84

Equation

A = L*w

Solution

x(x + 5) = 84 Remove the brackets

x^2 + 5x = 84 Subtract 84 from both sides

x^2 + 5x - 84 = 0 This will factor

(x - 7)(x + 12) =0

x + 12 has no meaning. Geometry does not use negative numbers.

x - 7 = 0 Add 7 to both sides

x = 7

The width = 7

The length = 7 + 5 = 12