WAEC - Mathematics (1996 - No. 32)
In the diagram, ∠PMN = ∠PRQ and ∠PNM = ∠PQR. If /Pm/ = 3cm, /MQ/ = 7cm and /PN/ = 5cm, find /NR/
1cm
3cm
31/2
5cm
6cm
Explicació
△PQR is similar to △PNM
\(\frac{PQ}{PN}\) = \(\frac{PR}{PM}\)
\(\frac{7 + 3 }{5}\) \(\frac{5 + NR}{3}\)
cross multiply
10 x 3 = (5 x 5) + 5 x NR
5NR = 30 - 25 = 5
NR = \(\frac{5}{5}\) = 1 cm.