Question

6. The diagonal of a rectangular field i
60 metres more than the shorter side
If the longer side is 30 metres more
than the shorter side, find the sides of
the field.
(AS
​

Answer 1

$\huge\bold{\mathtt {\purple{ A{\pink{ N{\green{ S {\blue{ W{\red{ E{\orange{ R}}}}}}}}}}}}}$

ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟ ᴏғ ᴀ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ғɪᴇʟᴅ ɪ

60 ᴍᴇᴛʀᴇs ᴍᴏʀᴇ ᴛʜᴀɴ ᴛʜᴇ sʜᴏʀᴛᴇʀ sɪᴅᴇ

ɪғ ᴛʜᴇ ʟᴏɴɢᴇʀ sɪᴅᴇ ɪs 30 ᴍᴇᴛʀᴇs ᴍᴏʀᴇ

ᴛʜᴀɴ ᴛʜᴇ sʜᴏʀᴛᴇʀ sɪᴅᴇ, ғɪɴᴅ ᴛʜᴇ sɪᴅᴇs ᴏғ

ᴛʜᴇ ғɪᴇʟᴅ.

$\mathfrak\pink{\underline{\underline{SolutiOn-}}}$

lєt thє lєngth σf thє shσrtєr sídє вє х mєtrєs. 

thє lєngth σf thє díαgσnαl= 60 + х mєtrєs

thє lєngth σf thє lσngєr sídє = 30 + х mєtrєs

αpplчíng pчthαgσrαs thєσrєm, 

díαgσnαl² = sídє² + shσrtєr sídє²

(60+х)² = (30 + х)² + х²

3600 + 120х+х² = 900 + 60х + х² + х²

2700 + 60х - х² = 0

2700 + 90х - 30х - х² = 0

90(30 + х)- х(30 + х) = 0

х = 90, 

shσrtєr sídє ís 90m,  lσngєr sídє ís 90+30=120m

Answer 2

$\huge\bold{\mathtt{\purple{ A{\pink{\ N{\green{ S{\blue{ W{\red{ E{\orange{ R}}}}}}}}}}}}}$

ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟ ᴏғ ᴀ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ғɪᴇʟᴅ ɪ

60 ᴍᴇᴛʀᴇs ᴍᴏʀᴇ ᴛʜᴀɴ ᴛʜᴇ sʜᴏʀᴛᴇʀ sɪᴅᴇ

ɪғ ᴛʜᴇ ʟᴏɴɢᴇʀ sɪᴅᴇ ɪs 30 ᴍᴇᴛʀᴇs ᴍᴏʀᴇ

ᴛʜᴀɴ ᴛʜᴇ sʜᴏʀᴛᴇʀ sɪᴅᴇ, ғɪɴᴅ ᴛʜᴇ sɪᴅᴇs ᴏғ

ᴛʜᴇ ғɪᴇʟᴅ.

$\mathfrak\pink{\underline{\underline{SolutiOn-}}}$

lєt thє lєngth σf thє shσrtєr sídє вє х mєtrєs.

thє lєngth σf thє díαgσnαl= 60 + х mєtrєs

thє lєngth σf thє lσngєr sídє = 30 + х mєtrєs

αpplчíng pчthαgσrαs thєσrєm,

díαgσnαl² = sídє² + shσrtєr sídє²

(60+х)² = (30 + х)² + х²

3600 + 120х+х² = 900 + 60х + х² + х²

2700 + 60х - х² = 0

2700 + 90х - 30х - х² = 0

90(30 + х)- х(30 + х) = 0

х = 90,

shσrtєr sídє ís 90m, lσngєr sídє ís 90+30=120m