Question

What is the value of q?

Answer 1

2√14

Explanation:

ΔSQR and ΔTSR are similar. Therefore the sides are in proportion:

`(SR)/(QR)=(TR)/(SR)`

We have:

SR = q

QR = 10 + 4 = 14

TR = 4

Substitute:

`(q)/(14)=(4)/(q)` cross multiply

`(q)(q)=(14)(4)\\\\q^2=56\to q=√(56)\\\\q=√(4\cdot14)\\\\q=\sqrt4\cdot√(14)\\\\q=2√(14)`