Question

17. The perimeter of a rectangle is 86 centimeters. The length is 2 centimeters longer than the

width, w. What is the width?
White an equation that could be used to find the width of the rectangle.

Answer 1

perimeter = 2L + 2w

so 86 = 2L + 2w

if the length is 2cm longer than the width, that means w+2=L

plug this back into our original equation to get 2(w+2) + 2w = 86

distribute terms to get 4w + 4 = 86

4w = 82

w = 20.5cm

Answer 2

According to the problem, the length is 2 centimetres longer than the width, so the length can be expressed as:

l = w + 2

length = width + 2

The perimeter of a rectangle is twice the sum of its length and width, so we can set up an equation to represent the perimeter given in the problem:

P = 2(l + w)

Substituting the expression for l in terms of w, we get:

P = 2((w + 2) + w)

Simplifying this expression, we get:

P = 2(2w + 2)

P = 4w + 4

We know that the perimeter of the rectangle is 86 centimetres, so we can substitute this value into the equation:

86 = 4w + 4

Subtracting 4 from both sides:

82 = 4w

Dividing both sides by 4:

w = 20.5

Therefore, the width of the rectangle is 20.5 centimetres.

The equation that could be used to find the width of the rectangle is:

4w + 4 = 86

where w represents the width of the rectangle in centimetres.