Question

The area of trapezium is 180 sqcm and it's height is 9 Cm. If one of the parallel side is longer than the other by 6 Cm, the length of the longer of the parallel sides is?

Answer 1

Answer:

Given;

area of the trapezium= 180 sq. cm

h= 9cm.

Step-by-step explanation:

let, one parallel side be X.

another side be X+6 cm

area of a trapezium = 1/2 ×(sum of parallel side)×h

= now, 1/2 × (X+ X+ 6) × 9=180

= 1/2×(2X+6)×9=180

= X+6×9=180

=X+54=180

=X= 180- 54=126cm.

hence ,one side is 126.

another side is 126+ 6=132cm.(ans).

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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