The length of a rectangle is 10 mm longer than its width. Its perimeter is more than 80 mm. Let w equal the

width of the rectangle.

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

(b) Use these expressions to write an inequality based on the given information.

(c) Solve the inequality, clearly indicating the width of the rectangle

We know that the length (L) of the rectangle in question is 7mm longer than its width (W). Let's represent that as the following:

L=7+W

A rectangle's perimeter (the total sum of its sides) will be made my 2 sides representing the length (2L) and 2 sides representing the width (2W). We also know that this rectangle's perimeter is greater than 62. Since eventually we are solving for W, let's state all expressions in terms of W:

2L=2 (7+W)

2 (7+W) + 2W>62

14+2W+2W>62

14+4W>62

4W>62-14

4W>48

W>48/4

W>12

If the rectangle's perimeter is greater than 62, then the width will be greater than 12. Let's confirm this:

Perimeter=2L+2W

P=2 (7+12) + 2 (12)

P=14+24+24

P=62

So we can see that if the perimeter is to surpass 62, W needs to be greater than 12 and L (which is also 7+W) needs to be greater than 19.

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

P>80

2 (L+W) >80

divide 2

L+W>80

L is 10 more than W

L=10+W

A. L=10+W

B. L+W>80

C.

L+W>80

sub L=10+W

10+W+W>80

minus 10

2W>70

divid 2

W>35

W is mor than 35