Question

The area of trapezium is 180cm sqare and its height is 9 cm.If one of the parallel sides is longer than the other by 6 cm the length of the longer of the parallel sides is :

Answer 1

area=0.5(a+b)h

180 =0.5(a+a+6)9

2a+6=40

a=17

length of longer side is 17+6=23

Answer 2

ɢɪᴠᴇɴ :-

ᴀʀᴇᴀ ᴏꜰ ᴛʜᴇ ᴛʀᴀᴘᴇᴢɪᴜᴍ = 180 ᴄᴍ²

ʜᴇɪɢʜᴛ ᴏꜰ ᴛʜᴇ ᴛʀᴀᴘᴇᴢɪᴜᴍ = 9 ᴄᴍ

ᴏɴᴇ ꜱɪᴅᴇ ɪꜱ ʟᴏɴɢᴇʀ ᴛʜᴀɴ ᴛʜᴇ ᴏᴛʜᴇʀ ʙʏ = 6 ᴄᴍ

ᴛᴏ ꜰɪɴᴅ :-

ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ.

ꜱᴏʟᴜᴛɪᴏɴ :-

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

ʜ = ʜᴇɪɢʜᴛ

ʟ = ʟᴇɴɢᴛʜ

ʙ = ʙʀᴇᴀᴅᴛʜ

ɢɪᴠᴇɴ ᴛʜᴀᴛ,

ʜᴇɪɢʜᴛ = 180 ᴄᴍ²

ʜᴇɪɢʜᴛ = 9 ᴄᴍ

ᴏɴᴇ ꜱɪᴅᴇ ɪꜱ ʟᴏɴɢᴇʀ ᴛʜᴀɴ ᴛʜᴇ ᴏᴛʜᴇʀ ʙʏ = 6 ᴄᴍ

ʟᴇᴛ ᴜꜱ ᴄᴏɴꜱɪᴅᴇʀ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴏᴛʜᴇʀ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇ ᴛᴏ ʙᴇ x

ᴛʜᴇɴ, ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴏᴛʜᴇʀ ꜱɪᴅᴇ ᴡɪʟʟ ʙᴇ (x + 6) ᴄᴍ

ᴀʀᴇᴀ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ = ½ × ꜱᴜᴍ ᴏꜰ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ × ᴅɪꜱᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ.

ᴀʀᴇᴀ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ = 1/2 × 9 × (x+x+6)

⟹180 = 1/2 × 9 × (x+x+6)

⟹360=18x+54

ꜰɪɴᴅɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏꜰ x,

⟹18x=360−54

⟹18x=306

⟹x= 306/18

⟹x=17

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏꜰ x ɪꜱ 17

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ, ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴏᴛʜᴇʀ ꜱɪᴅᴇ ɪꜱ x + 6

ʙʏ ꜱᴜʙꜱᴛɪᴛᴜᴛɪɴɢ 17 ɪɴ x,

⟹17+x=23

ᴛʜᴇʀᴇꜰᴏʀᴇ, ᴛʜᴇ ᴛᴡᴏ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ ᴀʀᴇ 17 ᴄᴍ ᴀɴᴅ 13 ᴄᴍ

ᴛᴏ ɴᴏᴛᴇ :-

ᴛʜᴇ ꜰᴏʀᴍᴜʟᴀ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴀʀᴇᴀ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ ɪꜱ:

ᴀʀᴇᴀ = ½ × ꜱᴜᴍ ᴏꜰ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ × ᴅɪꜱᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ

ᴘʀᴏᴘᴇʀᴛɪᴇꜱ ᴏꜰ ᴀ ᴛʀᴀᴘᴇᴢɪᴜᴍ ɪɴᴄʟᴜᴅᴇꜱ:

ᴀ ᴛʀᴀᴘᴇᴢɪᴜᴍ ʜᴀꜱ 4 ᴜɴᴇQᴜᴀʟ ꜱɪᴅᴇꜱ: ᴛᴡᴏ ᴘᴀʀᴀʟʟᴇʟ ᴀɴᴅ ᴛᴡᴏ ɴᴏɴ-ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ.

ꜱᴜᴍ ᴏꜰ ᴀʟʟ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇꜱ ɪꜱ 360 ᴅᴇɢʀᴇᴇꜱ.

ᴅɪᴀɢᴏɴᴀʟꜱ ʙɪꜱᴇᴄᴛ ᴇᴀᴄʜ ᴏᴛʜᴇʀ.

____________________________________________