.(a) In APQR, ∠PQR= 90°. If its area is 216cm\(^2\) and |PQ|:|QR| is 3:4, find |PR|.
(b) The present ages of a man and his son are 47 years and 17 years respectively. In how many years would the man's age be twice that of his son?
(a) \(\frac{1}{2}\)IPQ||gr|= 216
\(\frac{|PQ|}{|QR|}\) = \(\frac{3}{4}\)
PQ= \(\frac{3}{4}\)
\(\frac{1}{2}\) * \(\frac{3}{4}\)|QR|||QR| = 216
|QR|\(^2\) = \(\frac{216 * 4 * 2}{3}\)
|QR|= √576 = 24cm
|PQ| =\(\frac{3}{4}\) x 24 =18cm
|PR| = √(24\(^2\) + 18\(^2\)) = 30cm
(b) Let m be the number of years:
47 + m =2(17+m)
47 + m = 34 + 2m
2m - m = 47 - 34
m = 13 years
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