Math, asked by rajnibalaett, 10 months ago

∆ABC is an equilateral ∆ with perimeter 60 cm. S and R are points on sides AB and AC respectively. P and Q are

points on Side BC Further, SR//BC, Sp//AC, RQ//AB and SR + SP + RQ =25cm. Find the length of PQ.​

Answers

Answered by amitnrw
0

Length of PQ.​ = 10 cm

Step-by-step explanation:

∆ABC is an equilateral ∆ with perimeter 60 cm.

=> Side of ∆ABC = 60/3 = 20 cm

SR//BC

=> ΔASR ≈ ΔABC

=>  ΔASR is equialaterla triangle

Let say SR = x cm

=> AS =  AR = SR = x  cm

=> BS = 20 - x cm

CR = 20 - x xm

as  SP//AC, RQ//AB

=> ΔBSP ≈ ΔBAC  &  ΔCRQ ≈ ΔCAB

=>  ΔBSP & ΔCRQ are equilateral traingle

=> SP = BS = 20 - x cm

  QR = CR = 20 - x  cm

SR + SP + RQ = 25 cm

=> x + 20-x + 20 -x = 25

=> x = 15 cm

BP + PQ + QC  = BC

=> BS + PQ + CR = 20

=> 20 -x  + PQ  + 20 - x = 20

=> PQ = 2x - 20

x = 15

=> PQ = 2 * 15 - 20

=> PQ = 10

length of PQ.​ = 10 cm

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