Rectangles are drawn on line segments of fixed lengths. When the breadths are 6 m
and 5 m respectively the sum of the areas of the rectangles is 83 m2. But if the breadths
are 5 m and 4 m respectively the sum of the areas is 68 m2. Find the sum of the areas
of the squares drawn on the line segments.
Answers
❥︎❥︎ANSWER☃️✨࿐
ʟᴇᴛ ʟᴇɴɢᴛʜ ᴏғ ғɪʀsᴛ ʀᴇᴄᴛᴀɴɢʟᴇ = xᴍ
ᴀɴᴅ
ʟᴇɴɢᴛʜ ᴏғ sᴇᴄᴏɴᴅ ʀᴇᴄᴛᴀɴɢʟᴇ =
ʏᴍ
ᴀɴᴅ
ᴡᴇ ᴋɴᴏᴡ ᴀʀᴇᴀ ᴏғ ʀᴇᴄᴛᴀɴɢʟᴇ =
ʟᴇɴɢᴛʜ × ʙʀᴇᴀᴅᴛʜ ,
sᴏ,
ᴀʀᴇᴀ ᴏғ ғɪʀsᴛ ʀᴇᴄᴛᴀɴɢʟᴇ = 6x
ᴀɴᴅ
ᴀʀᴇᴀ ᴏғ sᴇᴄᴏɴᴅ ʀᴇᴄᴛᴀɴɢʟᴇ = 5ʏ
ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ғɪʀsᴛ ᴄᴏɴᴅɪᴛɪᴏɴ ᴡᴇ ɢᴇᴛ
6x + 5ʏ = 83 ---------------- ( 1 )
ɴᴏᴡ ʙʀᴇᴀᴅᴛʜ ᴏғ ғɪʀsᴛ ʀᴇᴄᴛᴀɴɢʟᴇ = 5 ᴍ ᴀɴᴅ ʙʀᴇᴀᴅᴛʜ ᴏғ sᴇᴄᴏɴᴅ ʀᴇᴄᴛᴀɴɢʟᴇ = 4 ᴍ
sᴏ,
ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ sᴇᴄᴏɴᴅ ᴄᴏɴᴅɪᴛɪᴏɴ ᴡᴇ ɢᴇᴛ
5x + 4ʏ = 68 --------------------- ( 2 )
ɴᴏᴡ ᴡᴇ ᴍᴜʟᴛɪᴘʟᴇ ᴇǫᴜᴀᴛɪᴏɴ 1 ʙʏ 4 , ᴀɴᴅ ɢᴇᴛ
24x + 20ʏ = 332 ------------------- ( 3 )
ᴀɴᴅ
ᴍᴜᴛɪᴘʟʏ ʙʏ 5 ɪɴ ᴇǫᴜᴀᴛɪᴏɴ 2, ᴡᴇ ɢᴇᴛ
25x + 20ʏ = 340 -------------------- ( 4 )
ɴᴏᴡ ᴡᴇ sᴜʙᴛʀᴀᴄᴛ ᴇǫᴜᴀᴛɪᴏɴ 3 ғʀᴏᴍ ᴇǫᴜᴀᴛɪᴏɴ 4 ᴀɴᴅ ɢᴇᴛ
x = 8 , sᴜʙsᴛɪᴛᴜᴛᴇ ᴛʜᴀᴛ ᴠᴀʟᴜᴇ ɪɴ ᴇǫᴜᴀᴛɪᴏɴ 2 ᴡᴇ ɢᴇᴛ
5 ( 8 ) + 4ʏ = 68
4ʏ = 28
ʏ = 7
sᴏ,
ʟᴇɴɢᴛʜ ᴏғ ғɪʀsᴛ ʀᴇᴄᴛᴀɴɢʟᴇ = 8ᴍ ᴀɴᴅ ᴡᴇ ᴅʀᴀᴡ ᴀ sǫᴜᴀʀᴇ ᴏɴ ᴛʜɪs ʙᴀsᴇ sᴏ , ᴀʀᴇᴀ ᴏғ ᴛʜɪs sǫᴜᴀʀᴇ = 82 = 64 ᴍ2
ᴀɴᴅ
ʟᴇɴɢᴛʜ ᴏғ sᴇᴄᴏɴᴅ ʀᴇᴄᴛᴀɴɢʟᴇ = 7ᴍ ᴀɴᴅ ᴡᴇ ᴅʀᴀᴡ ᴀ sǫᴜᴀʀᴇ ᴏɴ ᴛʜɪs ʙᴀsᴇ sᴏ , ᴀʀᴇᴀ ᴏғ ᴛʜɪs sǫᴜᴀʀᴇ = 72 = 49 ᴍ2
ᴛʜᴇɴ sᴜᴍ ᴏғ ᴀʀᴇᴀ ᴏғ ᴛʜᴇsᴇ ᴛᴡᴏ sǫᴜᴀʀᴇ = 64 + 49 = 113 ᴍ2.