Question

4) The perimeters of a square and
rectangle are equal. The area of the
square is 36 cm². If the length of the
rectangle is twice its breadth, what are
the dimensions of the rectangle?​

Answer 1

Answer:

4 cm & 8 cm

Step-by-step explanation:

Area of square = side²

=> 36 cm² = side²

=> √36cm² = side

=> 6 cm = side, therefore,

=> perimeter of square = 4side = 4(6cm)

= 24 cm

Let the the breadth of rectangle be x and then length should be 2x. Perimeter of rectangle is 2(length+breadth) = 2(2x+x)

= 6x

Since perimeters are equal:

6x = 24 cm => x = 24/6 = 4 cm

Therefore,

Breadth = x = 4 cm

Length = 2x = 2(4cm) = 8 cm

Answer 2

Answer:

✯ Given :-

• The perimeter of a square and rectangle are equal. The area of the square is 36 cm². The length of the rectangle is twice its breadth.

✯ To Find :-

• What are the dimensions of the rectangle ?

✯ Solution :-

Let, breadth of the rectangle be x cm

And, the length of the rectangle be 2x cm

➣ According to the question,

⇒ Area of the square = 36 cm²

⇒ side × side = 36

⇒ (side)² = 36

⇒ side = $\sqrt{36}$

➠ side = 6 cm

➔ We know that,

$\boxed{\bold{\large{✰\:Perimeter\: of\: square\: =\: Perimeter\: of\: rectangle\:✰}}}$

⇒ 4 × side = 2(l + b)

⇒ 4 × 6 = 2(2x + x)

⇒ 24 = 2(3x)

⇒ 24 = 6x

⇒ x = $\sf\dfrac{\cancel{24}}{\cancel{6}}$

➥ x = 4 cm

$\therefore$ ❖ The breadth of the rectangle = x = 4 cm

❖ The length of the rectangle = 2x = 2(4) = 8 cm.

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