A) 91 cm
B) 60 cm
C) 51 cm
D) 70cm
Correct Answer: C
Solution :
Given, AC = 21 cm, AB = 30 cm \[\because \]Q is mid-point of AC \[\therefore \]\[AQ=\frac{AC}{2}=\frac{21}{2}cm\] ?(i) \[\because \]R is mid-point of AB \[AR=\frac{AB}{2}=\frac{30}{2}cm\] ?(ii) In\[\Delta BCA,\] P is mid-point of BC, R is mid-point of Ba then, by mid-point theorem, \[PR||AC\]and \[PR=\frac{1}{2}AC=\frac{21}{2}\] ?(iii) Similarly, Q is mid-point of AC, P is mid-point of BC, then \[QP||AB\]and \[QP=\frac{1}{2}AB=\frac{30}{2}\] ?.(iv) \[\therefore \]Perimeter of quad. ARPQ \[=AR+RP+PQ+AQ\] \[=\frac{30}{2}+\frac{21}{2}+\frac{30}{2}+\frac{21}{2}\](from (i), (ii), (iii) and (iv)) \[=2.\frac{30}{2}+2.\frac{21}{2}=30+21=51\,cm.\]
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