Question

Q.2:- In a AABC, D and E are points on the sides AB and AC respectively such that DE||BC.
i) If AD = 4x-3, AE = x+2, BD = 3x - 1 and CE = 5x-3, find the value
x.​

Answer 1

ᴛʜᴇ ʙᴀsɪᴄ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟɪᴛʏ ᴛʜᴇᴏʀᴇᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ɪғ ᴀ ʟɪɴᴇ ɪs ᴅʀᴀᴡɴ ᴘᴀʀᴀʟʟᴇʟ ᴛᴏ ᴏɴᴇ sɪᴅᴇ ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴀɴᴅ ɪᴛ ɪɴᴛᴇʀsᴇᴄᴛs ᴛʜᴇ ᴏᴛʜᴇʀ ᴛᴡᴏ sɪᴅᴇs ᴀᴛ ᴛᴡᴏ ᴅɪsᴛɪɴᴄᴛ ᴘᴏɪɴᴛs ᴛʜᴇɴ ɪᴛ ᴅɪᴠɪᴅᴇs ᴛʜᴇ ᴛᴡᴏ sɪᴅᴇs ɪɴ ᴛʜᴇ sᴀᴍᴇ ʀᴀᴛɪᴏ.

ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴀᴅ=4x−38, ʙᴅ=3x−1, ᴀᴇ=8x−7 ᴀɴᴅ ᴄᴇ=5x−3. ʟᴇᴛ ᴀᴄ=x

ᴜsɪɴɢ ᴛʜᴇ ʙᴀsɪᴄ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟɪᴛʏ ᴛʜᴇᴏʀᴇᴍ, ᴡᴇ ʜᴀᴠᴇ

ʙᴅᴀᴅ=ᴀᴄᴀᴇ⇒3x−14x−3=x8x−5⇒x(4x−3)=(3x−1)(8x−5)⇒4x2−3x=3x(8x−5)−1(8x−5)⇒4x2−3x=24x2−15x−8x+5⇒4x2−3x=24x2−23x+5⇒24x2−23x+5−4x2+3x=0⇒20x2−20x+5=0⇒5(4x2−4x+1)=0⇒4x