Question

The width of a rectangle is 52 centimeters. The perimeter is at least 734. Write and solve an inequality to find the possible lengths of the rectangle.

A) l ≤ 15 cm
B) l ≥ 15 cm
C) l ≤ 29 cm
D) l ≥ 29 cm

Answer 1

The possible lengths of the rectangle are l ≥ 315 cm.

Step-by-step explanation:

To find the possible lengths of the rectangle, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. In this case, the width is given as 52 centimeters and the perimeter is at least 734.

Substituting the values into the formula, we have:

734 ≥ 2l + 2(52)

734 ≥ 2l + 104

Subtracting 104 from both sides:

630 ≥ 2l

Dividing both sides by 2:

315 ≥ l

Therefore, the possible lengths of the rectangle are l ≥ 315 cm. Option D) l ≥ 29 cm is the correct answer.