Question

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

Answer 1

area = 180 cm sq
h =9cm
a= x+ 6
b=x
area =1/2(a+b)×h
180 = 1/2(x+6+x)×9
180/9 = 1/2×(2x+6)
20×2/1= 2x+6
40 = 2x+6
40-6 =2x
32=2x
32/2=x
16 =x
16+6 = x+6
22 = x+6
one side is 16cm and other is 22 cm

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.

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