Question

Find the side and perimeter
of
square whose diagonal is 10 cm.​

Answer 1

Aɴsᴡᴇʀ:

• The side of square = 5√2 cm
• The perimeter of square = 20√2 cm

Gɪᴠᴇɴ:

• A square whose diagonal is 10 cm.

Nᴇᴇᴅ Tᴏ Fɪɴᴅ:

• The side of square = ?
• The perimeter of square = ?

Solution:

Bʏ ᴛʜᴇ Pʏᴛʜᴀɢᴏʀᴀs Tʜᴇᴏʀᴇᴍ:

In Triangle ABD,

➦ AB² + AD² = BD²

➦ a² + a² = 10²

➦ 2a² = 100

➦ a² = 50

➦ a = √50

➦ a = 5√2 cm

Hᴇɴᴄᴇ:

• The side of square is 5√2 cm.

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Nᴏᴡ,

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ ʜᴇʀᴇ:

• Perimeter of square = 4 × side

Pᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇs:

➦ Perimeter of square = 4 × a

➦ Perimeter of square = 4 × 5√2 cm

➦ Perimeter of square = 20√2 cm

Tʜᴇʀᴇғᴏʀᴇ:

• The perimeters of square is 20√2 cm.

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