In a quadrilateral PQRS,PQRS, if PQRS,S=2Q,PS=qPQRS,S=2Q,PS=q and RS=p.RS=p. Find the length of the side PQ.PQ.


Answer:

p+qp+q

Step by Step Explanation:
  1. Let us first draw the quadrilateral PQRSPQRS.
      P Q R S 2x x E
    Let Q=xQ=x
    So, S=2xS=2x
    Let us join RR to a point EE on the side PQPQ such that PERSPERS is a parallelogram.
  2. We know that opposite sides of a parallelogram are equal.
    So, PSR=PER=2x(i)PSR=PER=2x(i)
  3. Also, PER+REQ=180[ Angles on a straight line ]REQ=180PERREQ=1802x[From (i)]
  4. The sum of angles of a triangle is 180.
    In ERQ REQ+EQR+QRE=1801802x+x+QRE=180QRE=x
  5. In ERQ, QRE=EQRER=EQ(ii)[ Sides opposite to equal angles are equal. ]
  6. We are given that RS=p and PS=q.
    As, opposite sides of a parallelogram are equal,
    RS=PE=p
    and PS=ER=q
    EQ=q[From (ii)]
  7. We can see that PQ=PE+EQ=p+q
  8. Thus, PQ=p+q

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