1

Problem

The perimeter of a rectangle is equal to the perimeter of a square. If the side length of the square is 7 cm, find the dimensions (length and width) of the rectangle?

2

Step

The side (s)length of the square is given,

7 cm

3

Step

Perimeter of square(p)

p = 4s
p = 4 * 7 = 28 cm

4

Hint

We must find the rectangle’s dimensions as its perimeter is the same as the square’s. We’ll need to check the options.

5

Step

Here option A values are Length = 9 cm, and Width = 6 cm

p = 2(l+ w) = 2(9 + 6) = 30 cm

6

Hint

In this scenario, the perimeter of the rectangle is 30 cm and the perimeter of the square is 28 cm, indicating they do not match.

7

Step

Similarly, option B values are Length = 9cm and width = 5cm.

p = 2(l+ w) = 2(9 + 5)=2(14) = 28 cm

8

Step

In this scenario, both the perimeter of the rectangle and the perimeter of the square are 28 cm, indicating that they match.

9

Step

Similarly, option C values are Length = 10cm and width = 7cm.

p = 2(l+ w) = 2(10 + 7) = 34 cm

10

Step

In this scenario, the perimeter of the rectangle is 30 cm and the perimeter of the square is 28 cm, indicating they do not match.

11

Step

Similarly, option D values are Length = 10cm and width = 9cm.

p = 2(l+ w) = 2(10 + 9) = 38 cm

12

Step

In this scenario, the perimeter of the rectangle is 30 cm and the perimeter of the square is 28 cm, indicating they do not match.

13

Sumup

Please summarize steps

Choices

14

Choice-A

Substituting the option value into the problem reveals a perimeter inconsistent with that of a square, making it incorrect

Wrong Length = 9 cm, Width = 6 cm

15

Choice-B

Substituting the option value into the problem ensures satisfaction of the condition, as the perimeter matches that of a square, making it the correct choice

Correct Length = 9 cm, Width = 5 cm

16

Choice-C

Substituting the option value into the problem reveals a perimeter inconsistent with that of a square, making it incorrect

Wrong Length = 10 cm, Width = 7 cm

17

Choice-D

Substituting the option value into the problem reveals a perimeter inconsistent with that of a square, making it incorrect

Wrong Length = 10 cm, Width = 9 cm

18

Answer

option

B