Question

The perimeter of a rectangle is at most 24 cm. Two opposite sides are both 4 cm long. What are the possible lengths of the other two sides?

A.) Greater than 0 cm and less than or equal to 6 cm
B.) greater than 0 cm and less than or equal to 8 cm
C.) greater than 4 cm and less than or equal to 8 cm
D.) greater than 4 cm and less than or equal to 10 cm

Answer 1

The possible lengths of the other two sides of the rectangle are greater than 0 cm and less than or equal to 8 cm, making option B the correct answer.

Step-by-step explanation:

The student has asked about the possible lengths of the other two sides of a rectangle given that the rectangle's perimeter is at most 24 cm and two opposite sides are both 4 cm long. To solve for the possible lengths of the other two sides, we use the formula for the perimeter of a rectangle (P = 2l + 2w), where l is the length and w is the width.

Since the perimeter is at most 24 cm, the equation is 2(4) + 2w ≤ 24. Simplifying gives us 8 + 2w ≤ 24, and further simplifying yields w ≤ 8. The width must be greater than 0 cm, as the sides of a rectangle must have positive length, therefore the possible lengths of the other two sides are: greater than 0 cm and less than or equal to 8 cm.

Option B is the correct answer.