Question

The perimeter of the rectangle and square are
same. Length and breadth of the rectangle
are 10 cm and 8 cm respectively. What is the
area of the square?
a. 114 sq. cm b. 36 sq. cm
c. 81 sq. cm
d. 64 sq. cm
​

Answer 1

Step-by-step explanation:

All the answers mentioned before explained the simple way of solving this problem. And, there is no harm in opting for the safe method. However, there is another formula that can be used. It has been explained in detail below:

Perimeter of Square=Perimeter of Rectangle

=> 4x Side= 2L + 2B

Thus, Side= 2L + 2B /4

Or, Side= L + B /2

Now, Area of Square= Side x Side

Or, Area= (L + B /2) x (L + B /2)

We have done some simple transposition at the beginning, and formulated this equation. As we know, this only works if the perimeters of the Square and Rectangle are the same. Now, let us implement the same formula for the asked question, and add the given values:

L= 10 cm

B= 6 cm

Thus, Area of Square= (L + B /2) x (L + B /2)

=> (10 + 6 /2) x (10 + 6 /2)

=> 16/2 x 16/2

=> 8 x 8= 64 cm sqr.

As we can see, the Area is correct. We can verify this again, if needed. This formula can be used if you want to. But, I do not know whether it is allowed. I recommend writing the entire formula, and explaining it while solving. This will help the person who is checking the answer understand.

This formula is not commonly used, and I have checked it thoroughly for any loopholes. I still recommend using the basic formula, and keeping this for extra help. If there is any doubt, feel free to comment.

Answer 2

Answer:

$81 \: cm²$

Step-by-step explanation:

Perimeter of rectangle is = 2(+b)

=2(10+8)

=2(18)

= 36 cm.

Now, perimeter of square is 4(a),

where a is the side of square.

We have given that perimeter is

equal so equate 4(a) with the

perimeter of the rectangle, we get:

4(a) = 36

a = 9 cm

So the side of the square is 9cm.

Now area of sqare is 9×9=81.

So the area of the square is 81 cm².