Question

What is the value of x? x= ____ units

Answer 1

We have similar triangles RST ,TSR and TRQ.The triangles are similar to each other .

Similar triangles have sides in proportion.

In similar triangles TQR and TRS:

$\frac{TR}{ST} =\frac{TQ}{TR}$

Or,

$\frac{x}{9} =\frac{16}{x}$

Cross multiplying

$x^{2}=16(9)$

$x^{2}=144$

Taking root

x=12.

Answer 2

∵ ΔSRQ is a right triangle
and RT⊥SQ
∴ x² = ST * TQ
∴ x² = 9 *16 = 144

∴ x = √144 = 12