347,195 views
5 votes
5 votes
Please help with how to write the inequality! The length of a a rectangle is 8 more than twice the width. What can the width of the rectangle be so that the perimeter is under 30 cm?

User Rahul Hirve
by
2.5k points

1 Answer

18 votes
18 votes

Answer:

Here is answer

Explanation:

To write the inequality for this problem, we need to express the perimeter of the rectangle in terms of the width of the rectangle. The perimeter of the rectangle is the sum of all four sides, so it is equal to twice the sum of the length and the width:

Perimeter = 2 * (length + width)

We are given that the length of the rectangle is 8 more than twice the width, so we can substitute this expression for the length:

Perimeter = 2 * (2 * width + 8 + width)

= 2 * (3 * width + 8)

= 6 * width + 16

We are asked to find the values of the width that make the perimeter less than 30 cm. We can express this as an inequality by replacing the equals sign with a less than sign:

6 * width + 16 < 30

We can solve this inequality by subtracting 16 from both sides:

6 * width + 16 - 16 < 30 - 16

6 * width < 14

We can divide both sides of the inequality by 6 to find the possible values of the width:

(6 * width) / 6 < 14 / 6

width < 2.33...

The width of the rectangle must be less than 2.33... cm in order for the perimeter to be under 30 cm.

Note: It's important to remember that the width must be less than 2.33..., but not equal to it, in order to satisfy the inequality. This means that the width can be any value between 0 and 2.33..., but not 2.33... itself.

User Svestka
by
2.5k points