a) 21 m
b) 25 m
c) 16 m
d) 12 m

Answer: a
Explanation:

In $$\Delta $$STR, by Pythagoras theorem
$$\eqalign{ & R{T^2} = S{T^2} + R{S^2} \cr & S{T^2} = {15^2} – {9^2} = 144 \cr & ST = 12\,{\text{m}} \cr} $$
In $$\Delta $$TQP, by Pythagoras theorem
$$\eqalign{ & P{T^2} = T{Q^2} + P{Q^2} \cr & T{Q^2} = {15^2} – {12^2} = 81 \cr & TQ = 9\,{\text{m}} \cr} $$
Distance between houses
SQ = ST + TQ
SQ = 12 + 9
SQ = 21 m