Question

Solve and graph on a number line.

A. Find the length and the width of a rectangle when the width is 4 ft  shorter than the length. The perimeter of the rectangle is greater than 72 ft. 

Answer 1

• The formula for the perimeter of the rectangle P = 2(l + w), where l = length and w = width.

Let x be the length(l) of the rectangle.

The width(w) of the rectangle = 4 ft shorter than the length = x - 4.

The perimeter(P) of the rectangle is greater than 72 ft ⇒ P > 72.

2(l + w) > 72

2[ x + (x - 4) ] > 72

x + (x - 4) > 36

2x - 4 > 36

2x > 40

x > 20.

The length(l) of the rectangle is greater than 20 ft ⇒ l = x > 20.

Subtract 4 from each side of the above inequality.

x - 4 > 20 - 4

x - 4 > 16.

The width(w) of the rectangle is greater than 16 ft ⇒ w = x - 4 > 16.

Length : l  > 20 and Width : w  > 16.

The open circles means that 16, 20 and 72 are not a solutions of the inequality.

 

Answer 2

• The formula for the perimeter of the rectangle P = 2(l + w), where l = length and w = width.

Let x be the length(l) of the rectangle.

The width(w) of the rectangle = 4 ft shorter than the length = x - 4.

The perimeter(P) of the rectangle is greater than 72 ft ⇒ P > 72.

2(l + w) > 72

2[ x + (x - 4) ] > 72

x + (x - 4) > 36

2x - 4 > 36

2x > 40

x > 20.

The length(l) of the rectangle is greater than 20 ft ⇒ l = x > 20.

Subtract 4 from each side of the above inequality.

x - 4 > 20 - 4

x - 4 > 16.

The width(w) of the rectangle is greater than 16 ft ⇒ w = x - 4 > 16.

Length : l  > 20 and Width : w  > 16.

The open circles means that 16, 20 and 72 are not a solutions of the inequality.