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:

`(TR)/(ST) =(TQ)/(TR)`

Or,

`(x)/(9) =(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