In the diagram, ∠PMN = ∠PRQ and ∠PNM = ∠PQR. If /Pm/ = 3cm, /MQ/ = 7cm and /PN/ = 5cm, find /NR/
Attached Figure / Diagram
A
1cm
B
3cm
C
31/2
D
5cm
E
6cm
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
△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.
Source: WAEC / JAMB / NECO Classroom Archive (Record #23822)