Question

The perimeter of a rectangle is 38". If the

length is 3" more than the width, find the
width:
9-A 17 1/2"
9-B 8"
9-C
11"
9-D 14 1/2"

Answer 1

Width = 8"

Explanation:

2(t+w) = 38 Eq. 1

t = w+3 Eq. 2

t = length

w = width

From Eq. 2:

t+w = 38/2

t+w = 19

t = 19 - w Eq. 3

Replacing Eq. 3 in Eq. 2:

19 - w = w + 3

19 - 3 = w + w

16 = 2w

16/2 = w

w = 8

Frm Eq. 2:

t = w + 3

t = 8 + 3

t = 11

Check:

From Eq. 1

2(t+w) = 38

2(11+8) = 38

2(19) = 38

Answer 2

Length = 11" and width = 8".

Explanation:

let L be the length of the rectangle

and w be its width.

Formula (perimeter P of a rectangle) :

P = 2 × (L + w)

================================

Then

L = w + 3

and

P = 2 × (L + w)

= 2 × (w + 3 + w)

= 2 × (2w + 3)

= 4w + 6

Solving the equation P = 4w + 6 for w :

P = 4w + 6

⇔

38 = 4w + 6

⇔

32 = 4w

⇔

w = 32 ÷ 4

= 8

Determining the length L :

L = w + 3

⇔

L = 8 ÷ 3

= 11

Conclusion:

L = 11 and w = 8