Answer:
2√14
Step-by-step explanation:
ΔSQR and ΔTSR are similar. Therefore the sides are in proportion:
[tex]\dfrac{SR}{QR}=\dfrac{TR}{SR}[/tex]
We have:
SR = q
QR = 10 + 4 = 14
TR = 4
Substitute:
[tex]\dfrac{q}{14}=\dfrac{4}{q}[/tex] cross multiply
[tex](q)(q)=(14)(4)\\\\q^2=56\to q=\sqrt{56}\\\\q=\sqrt{4\cdot14}\\\\q=\sqrt4\cdot\sqrt{14}\\\\q=2\sqrt{14}[/tex]
