Question

The perimeter of square ABCD is 20 cm. What is the length of its diagonal AC? Hint 1 Find the side of the square, and then its diagonal. Hint 2 Use the Pythagoras Theorem in △ABC.

Answer 1

$\looparrowright$ Question :

➭Perimeter of sqare ABCD is 20cm.

➭What is length of Diagonal AC.

✞︎ Given :

• perimeter of sqaure = 20cm

☞ Hint 1 - Find the side of the square, and then its diagonal.

☞ Hint 2 - Use the Pythagoras Theorem in △ABC.

✞︎To Find :

• Length of Diagonal AC

$\looparrowright$ Solution :

✵ According to Hint - 1 ✵

$✯ \boxed{ \rm \: perimeter = 4 \times side}✯$

$\implies$ 20cm = 4 × side

• ✰ On transposing the terms :

$\implies \: \dfrac{20}{4} = \rm side$

$\therefore \boxed{\rm \: side = 5cm}$

• ✞︎ Now,

✵ According to Hint - 2 ✵

$\: \: \: \: \: \: \: \: \: \:$ ☕︎ Pythagoras Theorem :

$☞ \: \boxed{ \boxed{ \rm \: {h}^{2} = {p}^{2} + {b}^{2} }}$

☞ Here,

• p = 4cm

• b = 4cm

➪ H² = 5² + 5²

$\implies$ H² = 25 + 25

$\implies$ H² = 50cm

$\implies \rm \: {h}^{} = \sqrt{50}$

$\therefore$ H = 7.07cm

$\boxed{ \boxed{ \therefore{ \rm \:length \: of \: diagonal = 7.07cm}}}$