Question

The area of a square and the area of a rectangle are the same. The perimeter of the rectangle is 26 m. What is the area of the rectangle?

Answer 1

Answer :

Given : Area of square = Area of rectangle .

Let side of square = x , So,

Area of square = x²

Let sides of rectangle a and b , SO

Area of rectangle = ab
And
Perimeter of rectangle = 26

So,

2 ( Sum of both sides ) = 26 ( As we know Perimeter of rectangle = 2 ( Sum of both sides) )

So,

2 ( a + b ) = 26

a + b = 13

Here we know sum of both sides of rectangle = 13 ,

Now we take only integers value as length of side , and form different set , AS :

If length = 12 and width = 1 ,
So, Area of rectangle = 12 $\times$ 1 = 12 cm²

And

If length = 11 and width = 2 ,
So, Area of rectangle = 11 $\times$ 2 = 22 cm²

And

If length = 10 and width = 3 ,
So, Area of rectangle = 10 $\times$ 3 = 30 cm²
And

If length = 9 and width = 4 ,
So, Area of rectangle = 9 $\times$ 4 = 36 cm²
And

If length = 8 and width = 5 ,
So, Area of rectangle = 8 $\times$ 5 = 40 cm²

And

If length = 7 and width = 6 ,
So, Area of rectangle = 7 $\times$ 6 = 42 cm²

After that we get combination that gives same area as above we show in different length and width .

And

Area of square could be , As different integers value of x

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49

Now we can see that in both area , we can have only one common area , that is 36 .

SO,

Area of rectangle = 36 cm² ( Ans )