Question

True or false?
Two rectangles with the same perimeter can have different areas.
Explain your answer.
Thanks!

Answer 1

Answer: yes

Step-by-step explanation:

If a rectangle has a perimeter of, for example, 50, then all of the sides have to add up to 50. Also, bear in mind that opposite sides have to be the same.

If one rectangle has sides 5, 20, 5, 20, then the area would be 5 x 20 = 100

Another rectangle’s sides could be 10, 15, 10, 15, then the area would be 10 x 15 = 150

Answer 2

The given statement is true.

Important information:

• The given statement is "Two rectangles with the same perimeter can have different areas."

We need to check whether the given statement is true or false.

Rectangles:

Let the dimensions of a rectangle are 4 cm and 6 cm. Then the perimeter is:

$P_1=2(l+w)$

$P_1=2(4+6)$

$P_1=2(10)$

$P_1=20$

The area of the rectangle is:

$A_1=l\times w$

$A_1=6\times 4$

$A_1=24$

Let the dimensions of another rectangle are 8 cm and 2 cm. Then the perimeter is:

$P_2=2(8+2)$

$P_2=20$

The area of the rectangle is:

$A_2=8\times 2$

$A_2=16$

The perimeters of both rectangles are the same but the areas are different. Therefore, the given statement is true.

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