Question

The area of a trapezium is 126 square cm.The height of the trapezium is 7 cm.If one of the bases is longer than the other by 6 cm, find the lengths of the bases.

Answer 1

the area of trapezium 120 CM the height of a 71 20 CM square is equal to 77 squares into a b

Answer 2

ᴀɴꜱᴡᴇʀ :

• ʟᴇɴɢᴛʜ ᴏꜰ ʙᴀꜱᴇꜱ ᴀʀᴇ 15 ᴄᴍ ᴀɴᴅ 21 ᴄᴍ.

ꜱᴛᴇᴘ-ʙʏ-ꜱᴛᴇᴘ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:

ᴛᴏ ꜰɪɴᴅ :-

• ʟᴇɴɢᴛʜ ᴏꜰ ʙᴀꜱᴇꜱ.

ꜱᴏʟᴜᴛɪᴏɴ :-

ɢɪᴠᴇɴ ᴛʜᴀᴛ,

ᴀʀᴇᴀ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ ɪꜱ 126 ᴄᴍ².

ʜᴇɪɢʜᴛ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ ɪꜱ 7 ᴄᴍ.

ʟᴇᴛ, ᴏᴛʜᴇʀ ʙᴀꜱᴇ ʙᴇ x ᴄᴍ.

ᴀɴᴅ ᴏɴᴇ ʙᴀꜱᴇ ʙᴇ x + 6 ᴄᴍ.

ɪꜰ ᴛʜᴇ ʜᴇɪɢʜᴛ 7 ᴄᴍ ʜᴀᴠᴇ ᴛᴡᴏ ʙᴀꜱᴇꜱ ᴀɴᴅ ʜᴇɪɢʜᴛ ɪꜱ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ ᴛʜᴇɴ ᴛʜᴇ x ᴀɴᴅ x + 6 ᴀʀᴇ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ.

ᴡᴇ ᴋɴᴏᴡ,

ᴀʀᴇᴀ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ = (ᴀ + ʙ)/2 × ʜ

ᴘᴜᴛ ᴀʀᴇᴀ, ʜᴇɪɢʜᴛ ᴀɴᴅ ʙᴀꜱᴇꜱ (ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇꜱ) ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ ɪɴ ꜰᴏʀᴍᴜʟᴀ :

⟶ 126 = (x + x + 6)/2 × 7

⟶ 126 × 2 = 2x + 6 × 7

⟶ 252 = 2x + 6 × 7

⟶ 252/7 = 2x + 6

⟶ 36 = 2x + 6

⟶ 36 - 6 = 2x

⟶ 30 = 2x

⟶ 30/2 = x

⟶ x = 15

ʟᴇɴɢᴛʜ ᴏꜰ ʙᴀꜱᴇꜱ :-

ᴏɴᴇ ʙᴀꜱᴇ = x + 6 = 15 + 6 = 21 ᴄᴍ

ᴏᴛʜᴇʀ ʙᴀꜱᴇ = x = 15 ᴄᴍ