Question

I les triangle, P, Q and R are the mid-points
of the sides BC, CA and AB respectively. If
C16 cm, BC = 20 cm and AB = 24 cm,
find the perimeter of the quadrilateral
ARPQ
А​

Answer 1

Answer:

$In \: ΔABC \: </p><p></p><p>R \: and \: P \: are \: the \: midpoint \: of \: AB \: and \: BC \: \\ RP || AC, RP =  \frac{1}{2}  AC        [By \: midpoint \: theorem \\ In \: a \: quadrilateral \: \\ </p><p></p><p>[A \: pair \: of \: side \: is \: parallel \: and \: equal] \: \\ RP || AQ, RP = AQ \\ ∴R|| QA \:  is \: a \: parallelogram \\ </p><p></p><p></p><p></p><p>$

$AR =  \frac{1}{2} AB =  \frac{1}{2}  × 30 = 15 \: cm \\ AR = QP = 15                                                     [  ∵   Opposite \: sides \: are \: equal]  \\ ⇒ RP =  \frac{1}{2}  AC =  \frac{1}{2} × 21 = 10 .5cm           [   ∵  Opposite \: sides \: are \: equal]  \\ Now, \\ Perimeter \: of  \: ARPQ = AR + QP + RP + AQ \\ = 15 +15 +10.5 +10.5 \\ = 51cm$