Question

PQR and SQR are two right triangles with common hypotenuse QR if PR and SQ intersect at M such that PM=3cm,MR=6cm,SM=4cm,find the length of MQ

Answer 1

*See attachment

Prove that ΔPQM is similar to ΔSRM

∠QPM = ∠MSR (Both are 90º)

∠ PMQ = ∠ SMR (vertically opposite angles)

By AA property, ΔPQM is similar to ΔSRM

Using the property of similar figures:

PM/SM = MQ/MR

3/4 = MQ/6

4MQ = 3 x 6

4MQ = 18

MQ = 18 ÷ 4 = 4.5 cm

Answer: MQ = 4.5 cm