Question

What is the value of q?

Answer 1

Answer:

2√14

Step-by-step explanation:

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

$\dfrac{SR}{QR}=\dfrac{TR}{SR}$

We have:

SR = q

QR = 10 + 4 = 14

TR = 4

Substitute:

$\dfrac{q}{14}=\dfrac{4}{q}$                  cross multiply

$(q)(q)=(14)(4)\\\\q^2=56\to q=\sqrt{56}\\\\q=\sqrt{4\cdot14}\\\\q=\sqrt4\cdot\sqrt{14}\\\\q=2\sqrt{14}$