Question

The area of a square is 81 . Find its perimeter and the length of its diagonal

Answer 1

Gɪᴠᴇɴ :-

• Area of Square = 81 cm²

ᴛᴏ ғɪɴᴅ :-

• Perimeter

• Length of Diagonal

sᴏʟᴜᴛɪᴏɴ :-

We know that,

→ Area of Square = a²

So,

→ a² = 81

→ a = √81

→ a = 9 cm

Now,

➡ Side(a) of square = 9 cm

Now,

➡ Perimeter of Square = 4a

→ 4a = 4 × 9

→ 36 cm

➡ Length of diagonal = √2a

→ √2a = √2 × 9

→ 9√2 cm

Hence,

• Perimeter of Square = 36 cm

• Length of Diagonal = 9√2 cm

Answer 2

$\large{\sf{\underline{\red{Question:-}}}}$

The area of a square is 81 sq. units.

Find:

• Perimeter of the square
• Length of its diagonals

$\rule{400}{4}$

$\large{\sf{\underline{\red{Answer:-}}}}$

$\bf{\green{\underline{\large{Finding \:perimeter:-}}}}$

First we have to find the length of the side of square.

➠ Let the side of a square be x units.

➠ Then it's area = (x * x) sq. units = x² sq. units

$\mathtt{\underline{\blue{HERE,}}}$

➠ Area of square (x² sq. units) = 81 sq. units = 9² sq. units

➠Then, side of square (x units) = 9 units

Now we will find perimeter

➠ Perimeter = x + x + x + x units = 4x units = 4 * 9 units = 36 units.

$\rule{400}{4}$

$\bf{\green{\underline{\large{Finding \:diagonal:-}}}}$

Refer to the attachment

➠ Triangle ABC is right angled at A [By the property that angle between the sides of a square is 90°]

$\bf{\bold{\underline{In \:triangle\: ABC}}}$

➠ AB = x units

➠ AD = x units

➠BD = d units --------------> diagonal

$\bf{\underline{\bold{Apply\: Pythagoras\: theorem}}}$

➠(AB)² + (AD)² = (BD)²

$\implies$ x² + x² = d²

$\implies$ 2x² = d²

$\implies$ d = √(2x²)

$\implies$ d = √2 * x

$\mathtt{\underline{HERE,}}$

➠ Side = x = 9 units

➠ Diagonal = d = √2 * x = √2 * 9 ≈ 12.73 units

$\rule{400}{4}$

$\green{\underline{\large{\sf{Answer:-}}}}$

$\underline{\boxed{\large{\red{\bf{Perimeter\:=\:36\:units}}}}}$

$\underline{\boxed{\large{\red{\bf{Length\:of\:diagonals\:≈12.73\:units}}}}}$