Question

a rectangleis 20cm long and 10cm wide .A square with the same perimeter as this rectangle will have an area of
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Answer 1

perimeter of the sq. =perimeter of rectangle

perimeter is...2(l+b)

$2(20 + 10) \\ = 2(30) = 60cm$

$perimter \: of \: square = 60cm \\ side \: of \: sq. \: = \frac{60}{4} = 15cm$

area of a square = a×a

$15 \times 15 = 225 {cm}^{2}$

hope it's helpful

Answer 2

• Area of a square = 225 cm²

Given :–

• Length of a rectangle = 20 cm long.
• Breadth of a rectangle = 10 cm wide.
• A square with the same perimeter as this rectangle.

To Find :–

• Area of a square.

Solution :–

We know that,

Perimeter of a rectangle = 2(length + breadth) / 2(l + b)

We have,

• Length = l = 20cm.
• Breadth = b = 10cm.

$\longmapsto2(20 cm+ 10cm)$

$\longmapsto2(30 \: cm)$

$\longmapsto60 \: cm$

According to the condition,

Perimeter of a rectangle = Perimeter of a square

Perimeter of a rectangle = 60cm.

That means,

Perimeter of a square = 60cm.

So,

We know that,

Perimeter of a square = 4 × side

$\longmapsto 60 \: cm = 4 \times side$

$\longmapsto \cancel\dfrac{60}{4} \: cm = side$

$\longmapsto15 \: cm = side$

Side of a square is 15 cm.

Now, we have to find the area of a square.

Area of a square = (side)²

• side = 15 cm.

$\longmapsto { (15 \: cm) }^{2}$

$\longmapsto15 \: cm\times15 \: cm$

$\longmapsto225 \: {cm}^{2}$

Hence,

The area of a square is 225 cm².