Question

the perimeter of one square is 748 cm and that of another is 336 cm find the perimeter and the diagonal of a square which is equal in area of these two

Answer 1

1sᴛ sǫᴜᴀʀᴇ :

ᴘᴇʀɪᴍᴇᴛᴇʀ = 748 ᴄᴍ

4 × sɪᴅᴇ = 748 ᴄᴍ

sɪᴅᴇ = 748 / 4 ᴄᴍ = 187 ᴄᴍ

2ɴᴅ sǫᴜᴀʀᴇ :

ᴘᴇʀɪᴍᴇᴛᴇʀ = 336 ᴄᴍ

4 × sɪᴅᴇ = 336 ᴄᴍ

sɪᴅᴇ = 336 / 4 = 84 ᴄᴍ

ɴᴏᴡ, ᴀ/ǫ

ᴀʀᴇᴀ ᴏғ 3ʀᴅ sǫᴜᴀʀᴇ = ᴀʀᴇᴀ ᴏғ 1sᴛ sǫᴜᴀʀᴇ + ᴀʀᴇᴀ ᴏғ 2ɴᴅ sǫᴜᴀʀᴇ

ᴀʀᴇᴀ ᴏғ 3ʀᴅ sǫᴜᴀʀᴇ = ( 187 )² + ( 84 )²

ᴀʀᴇᴀ ᴏғ 3ʀᴅ sǫᴜᴀʀᴇ = 34969 + 7056

( sɪᴅᴇ )² = 42025

sɪᴅᴇ = 205 ᴄᴍ

sɪᴅᴇ ᴏғ 3ʀᴅ sǫᴜᴀʀᴇ = 205 ᴄᴍ

ɴᴏᴡ,

ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ 3ʀᴅ sǫᴜᴀʀᴇ = 4 × 205

= 820 ᴄᴍ

ᴅɪᴀɢᴏɴᴀʟ ᴏғ 3ʀᴅ sǫᴜᴀʀᴇ = 2 √sɪᴅᴇ = 2√205 ᴄᴍ

Answer 2

☞ Answer :

Perimeter of the required square = 820 cm.

☞ Given :

Perimeter of square (1) = 748 cm.

Perimeter of square (2) = 336 cm.

☞ To Find :

Perimeter of the required square (3).

☛ How To Find :

We know,

Side of square = Perimeter/4

∴ Side of square (1) = 748/4 = 187 cm.

∴ Area of square (1) = (side)² = (187)² =

34969 cm²

$\:$

Side of square (2) = 336/4 = 84 cm.

∴ Area of another square = (84)² = 7056 cm²

Now, sum of areas of squares = 34969 + 7056

= 42025 cm²

Again, area of square(3) = sum of areas of squares (1) & (2)

= 42025 cm²

∴ Side of third square = √42025

42025 = 205 cm

∴Perimeter of square (3) = 4 × side of square (3)

= 4 × 205 = 820 cm

∴ Perimeter of the required square = 820 cm.