Question

The length of a rectangle is 8 mm longer than its width. Its perimeter is more than 32 mm. Let w equal the width of the rectangle.

a. Write an expression for the length in terms of the width.

b. Use expressions for the length and width to write an inequality for the
perimeter, on the basis of the given information.

c. Solve the inequality, clearly indicating the width of the rectangle.

Answer 1

Part A

w = width

L = length

L = w+8 since the length is 8 mm longer than the width

Answer: w+8

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Part B

P = perimeter of rectangle

P = 2*(L+W) = 2L + 2W

We want the perimeter to be more than 32 mm, so we want P to be greater than 32

This means we write P > 32

Replace P with either 2(L+W) or 2L+2W. I'll pick 2L+2W

So we go from

P > 32

to

2L+2W > 32

After this, replace L with W+8 (refer to part A above)

We now have

2(W+8) + 2W > 32

Answer: 2(w+8) + 2w > 32

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Part C

Let's solve the inequality found in part B to get...

2(w+8) + 2w > 32

2w + 16 + 2w > 32

4w + 16 > 32

4w + 16-16 > 32-16 ....... subtracting 16 from both sides

4w > 16

4w/4 > 16/4 ......... dividing both sides by 4

w > 4

Answer: w > 4; The width of the rectangle must be larger than 4 mm