Question

find side of a rhombus whose diagonal is 16cm and 12cm

Answer 1

Answer :


ᴀʟʟ sɪᴅᴇs ᴏғ ᴀ ʀʜᴏᴍʙᴜs ᴀʀᴇ ᴇǫᴜᴀʟ ɪɴ ʟᴇɴɢᴛʜ.
ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟs ᴏғ ᴛʜᴇ ʀʜᴏᴍʙᴜs ɪɴᴛᴇʀsᴇᴄᴛ ᴀᴛ ᴀ 90 ᴅᴇɢʀᴇᴇ ᴀɴɢʟᴇ.
ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟs ᴀɴᴅ ᴛʜᴇ sɪᴅᴇs ᴏғ ᴛʜᴇ ʀʜᴏᴍʙᴜs ғᴏʀᴍ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇs.
ᴏɴᴇ ʟᴇɢ ᴏғ ᴛʜᴇsᴇ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇs ɪs ᴇǫᴜᴀʟ ᴛᴏ 8 ᴄᴍ ɪɴ ʟᴇɴɢᴛʜ.
ᴛʜᴇ ᴏᴛʜᴇʀ ʟᴇɢ ᴏғ ᴛʜᴇsᴇ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇs ɪs ᴇǫᴜᴀʟ ᴛᴏ 6 ᴄᴍ ɪɴ ʟᴇɴɢᴛʜ
ᴛʜᴀᴛ ᴡᴏᴜʟᴅ ʙᴇ ʜᴀʟғ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴇᴀᴄʜ ᴅɪᴀɢᴏɴᴀʟ.


ᴛʜᴇ sɪᴅᴇs ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ғᴏʀᴍ ᴛʜᴇ ʜʏᴘᴏᴛᴇɴᴜsᴇ ᴏғ ᴛʜᴇsᴇ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇs.
ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ɪs:
ʜʏᴘᴏᴛᴇɴᴜsᴇ sǫᴜᴀʀᴇᴅ = ᴏɴᴇ ʟᴇɢ sǫᴜᴀʀᴇᴅ ᴘʟᴜs ᴏᴛʜᴇʀ ʟᴇɢ sǫᴜᴀʀᴇᴅ.
ᴛʜɪs ᴍᴀᴋᴇs ᴛʜᴇ ʜʏᴘᴏᴛᴇɴᴜsᴇ sǫᴜᴀʀᴇᴅ ᴇǫᴜᴀʟ ᴛᴏ 8² + 6² = 64 + 36 = 100
ᴛʜᴇ ʜʏᴘᴏᴛᴇɴᴜsᴇ ɪs ᴛʜᴇ sǫᴜᴀʀᴇ ʀᴏᴏᴛ ᴏғ 100 ᴡʜɪᴄʜ ᴍᴀᴋᴇs ᴛʜᴇ ʜʏᴘᴏᴛᴇɴᴜsᴇ ᴇǫᴜᴀʟ ᴛᴏ 10.

Answer 2

Question:-

The lengths of the diagonals of a rhombus are 16cm and 12cm. then find the length of the side of rhombus

Solution:-

we know that diagonal of rhombus,bisect each other in right angle ( 90° ).

we also know that all sides of rhombus are equal ( of equal length ).

so, now

Let rhombus is ABCD

Let, diagonal of rhombus

BD = 16 cm and AC = 12 cm

means,

OD = 8 cm and AO = 6 cm

By pythagorus theorem

To find length of AD ( and all side of rhombus )

=> (AD)² = (OD)² + (AO)²

=> (AD)² = (8)² + (6)²

=> (AD)² = 64 + 36

=> (AD)² = 100

=> AD = √100

=> AD = 10 cm

Hence length of all side of rhombus

is 10 cm.

i hope it helps you.