the diagonal of a rectangular field is 60 metres more than the shorter side if the longer side if the longer side is 30 metre more than the the shorter side find the sides of the field
Answers
ʜᴇʏᴀ ᴍᴀᴛᴇ!!
ʜᴇʀᴇ ɪs ᴜʀ ᴀɴsᴡᴇʀ ⏬ ⏬
ʟᴇᴛ ᴛʜᴇ sʜᴏʀᴛᴇʀ sɪᴅᴇ ᴏғ ᴛʜᴇ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ғɪᴇʟᴅ ʙᴇ 'x' ᴍᴇᴛᴇʀs.
ᴛʜᴇʀᴇғᴏʀᴇ ᴛʜᴇ ʟᴏɴɢᴇʀ sɪᴅᴇ ᴡɪʟʟ ʙᴇ (x + 30) ᴍᴇᴛᴇʀs.
ᴀɴᴅ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟ ᴡɪʟʟ ʙᴇ (x + 60) ᴍᴇᴛᴇʀs.
ɴᴏᴡ, ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ϙᴜᴇsᴛɪᴏɴ
ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟ ᴅɪᴠɪᴅᴇs ᴛʜᴇ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ɪɴᴛᴏ ᴛᴡᴏ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇs ᴀɴᴅ ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟ ɪs ᴛʜᴇ ᴄᴏᴍᴍᴏɴ sɪᴅᴇ ᴏғ ᴛʜᴇ ᴛᴡᴏ ᴛʀɪᴀɴɢʟᴇs ᴀɴᴅ ɪᴛ ɪs ᴀʟsᴏ ᴛʜᴇ ʟᴏɴɢᴇsᴛ sɪᴅᴇ ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇs ɪ.ᴇ. ᴛʜᴇ ʜʏᴘᴏᴛᴇɴᴜsᴇ.
sᴏ, ʙʏ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ,
(ᴅɪᴀɢᴏɴᴀʟ)² = (sᴍᴀʟʟᴇʀ sɪᴅᴇ)² + (ʟᴏɴɢᴇʀ sɪᴅᴇ)²
(x + 60)² = (x)² + (x + 30)²
x² + 120x + 3600 = x² + x² + 60x + 900
x² + 60x - 120x + 900 - 3600 = 0
x² - 60x - 2700 = 0
x² - 90x + 30x - 2700 = 0
x(x - 90) + 30(x - 90) = 0
(x - 90) (x + 30) = 0
x = 90 ʙᴇᴄᴀᴜsᴇ x = - 30 ᴀs ʟᴇɴɢᴛʜ ᴄᴀɴɴᴏᴛ ʙᴇ ᴘᴏssɪʙʟᴇ.
sᴏ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ sʜᴏʀᴛᴇʀ sɪᴅᴇ ɪs 90 ᴍᴇᴛᴇʀs ᴀɴᴅ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ʟᴏɴɢᴇʀ sɪᴅᴇ ɪs 90 + 30 = 120 ᴍᴇᴛᴇʀs.