Question

The perimeter of a square ABCD is twice the perimeter of ΔPQR. Find the area of the square
ABCD.​

Answer 1

Answer:

The perimeter of a square ABCD is twice the perimeter of ΔPQR

perimeter of ∆ PQR = sum of all sides

=6 + 5 + 7

= 18 cm

The perimeter of a square ABCD is twice the perimeter of ΔPQR.

18 × 2 = perimeter of square ABCD

36 = perimeter of square ABCD

but,

formula of perimeter of square = 4× side

36 = 4× side

36/4 = side

9 = side

side of square ABCD = 9cm

area of square ABCD = side²

= (9)²

= 81 cm

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Answer 2

Given:

The sides of the triangle are,

• PR = 6 cm
• QR = 7 cm
• PR = 5 cm

According to the question,

• The perimeter of a square (ABCD) is twice the perimeter of ΔPQR

To find:

• The area of the square.

So, ATQ

⇒ 2 (perimeter of triangle QPR) = perimeter of the square

⇒ 2 (6 + 7 + 5) = Perimeter of square

⇒ 2 * (18) = Perimeter of square

⇒ 36 = Perimeter of square

• Thus, the perimeter of the square is 36 cm.

Now,

Finding the each side of the square,

The perimeter of the square = 4 * side

⇒ 36 = 4 * side

⇒ 36 ÷ 4 = side

[By transporting 4 to LHS]

⇒ 9 = side

∴ The side of the square is 9 cm.

Now,

The area of the square is = (side)² units sq.

= (9)²

= 81 cm sq.

Hence,

• The area of the square whose perimeter is twice of the ΔPQR is 81 cm sq.