Question

The length of a rectangle is four more than three times the width. If the perimeter of this rectangle is at least 70 square centimeters. Write an inequality that can be solved to find the width of the rectangle.

2(4+3w)+2(w)≥70
4+3w≤70
3+4w≥70
2(4+3w)+2(w)≤70

Answer 1

To find the width of the rectangle, write the inequality 2(3w + 4 + w) ≥ 70 and solve for w. The width of the rectangle is at least 7.75 centimeters.

Step-by-step explanation:

To find the width of the rectangle, we need to write an inequality based on the given information. Let w represent the width of the rectangle. The length of the rectangle is four more than three times the width, so the length is 3w + 4. The perimeter of a rectangle is given by the formula 2(length + width), so the inequality is:

2(3w + 4 + w) ≥ 70

Simplifying the inequality gives:

8w + 8 ≥ 70

Subtracting 8 from both sides:

8w ≥ 62

Dividing both sides by 8:

w ≥ 7.75

Therefore, the width of the rectangle is at least 7.75 centimeters.