Question

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

Answer 1

Given:

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

To find:

• Dimensions of Rectangle?

Solution:

⠀⠀⌬ Let breadth of rectangle be x cm.

⠀⠀⌬ Then, Length of rectangle is 2x cm.

Now,

According to the given Question:

Area of square = 36 cm²

side × side = 36

(side)² = 36

side = 6 cm

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Also,

Perimeter of square = Perimeter of rectangle

⇏ 4 × side = 2(l + b)

⇏4 × 6 = 2(2x + x)

⇏ 24 = 2(3x)

⇏ 24 = 6x

⇏ x = 24/6

⇏ x = 4

Therefore,

• Breadth of rectangle, x = 4 cm
• Length of rectangle, 2x = 8 cm

∴ Hence, Dimensions (length and breadth) of rectangle are 8 cm and 4 cm respectively.