Question

kendra planted a rectangular garden, as shown. which measurements could be the length and width of a rectangular garden with the same perimeter but a different area? a. 10 yards by 10 yards b. 2 yards by 10 yards c. 10 yards by 3 yards d. 4 yards by 10 yards

Explanation:

Step1: Calculate the perimeter of the original garden

The original garden is a rectangle with length \( l = 8 \) yd and width \( w = 5 \) yd. The formula for the perimeter of a rectangle is \( P = 2(l + w) \).
Substituting the values, we get \( P = 2(8 + 5) = 2\times13 = 26 \) yd.

Step2: Calculate the area of the original garden

The formula for the area of a rectangle is \( A = l\times w \).
Substituting the values, we get \( A = 8\times5 = 40 \) square yards.

Step3: Check the perimeter and area of each option

• Option A: Length \( = 10 \) yd, Width \( = 10 \) yd.

Perimeter: \( P = 2(10 + 10) = 2\times20 = 40 \) yd (not equal to 26 yd, so eliminate).

• Option B: Length \( = 10 \) yd, Width \( = 2 \) yd.

Perimeter: \( P = 2(10 + 2) = 2\times12 = 24 \) yd (not equal to 26 yd, so eliminate).

• Option C: Length \( = 10 \) yd, Width \( = 3 \) yd.

Perimeter: \( P = 2(10 + 3) = 2\times13 = 26 \) yd (equal to original perimeter).
Area: \( A = 10\times3 = 30 \) square yards (different from 40 square yards).

• Option D: Length \( = 10 \) yd, Width \( = 4 \) yd.

Perimeter: \( P = 2(10 + 4) = 2\times14 = 28 \) yd (not equal to 26 yd, so eliminate).

Answer:

C. 10 yards by 3 yards