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.
Answers
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
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.
____________________________________________
.