Question

A square and a rectangle are equal in area. The perimeter of the rectangle is 26cm. What is its area?

Answer 1

ANSWER -
area of square = area of rectangle

area of square = x^2

let length of rectangle be (a) cm and width be (b) cm.


area ofrectangle =a*b

perimeter of rectangle =26 cm

so

2(a+b)=26

a+b=13

if length =12 cm and width =1 cm

so,are of rectangle=12*1=12 cm^2

lif ength =11 cm

and width =2 cm

area of rectangle=11*2 =22 cm ^2

if length =10 cm and width =3 cm

so,are of rectangle=10*3=30 cm^2

if length =9 cm and width =4 cm

so,are of rectangle=9*4=36 cm^2

if length =8 cm and width =5 cm

so,are of rectangle=40 cm^2

if length =7 cm and width =6 cm

so,are of rectangle=42 cm^2

Area of sqauare can be found be

1^1=1 cm^2

2^2=4 cm^2

3^2=9 cm^2

4^2=16 cm^2

5^2=25 cm^2

6^2=36 cm^2

7^2=49 cm^2

there is one common area=36 cm^2

so,Area of square=area of rectangle=36 cm^2

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Answer 2

The perimeter of rectangle=26cm

so to find the area we need to know the length and breadth

so, let the length and breadth be a and b

now, perimeter=2(l+b)

26=2(a+b)

26/2=a+b

13=a+b

So,here we have got to know that the sum of length and breadth is equal to 13

now over here we will divide 13 by 2 so that we will get the length of one side

therefore, 13÷2=6.5

now we have got the length of one side which is 6.5

now area of square=(side)²

=(6.5)²

=42.25

therefore in this we have finded the area of square with the help of the perimeter of rectangle

don't be confused because area of square and rectangle are equal so if the area of square is 42.25cm then the area of rectangle also will be 42.25cm²

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