Question

In the given figure. If
seg PQ paralell seg Rs parallel TU
and PR-6, RT =3, QS=5
then what is the lenght
of SU?
choose the correct alternative options.
1)2.5 units 2)7.5 units 3)10 units 4) 15 units​

Answer 1

Answer:

The length of SU is 2.5 units.

Option ( 1 ) 2.5 units.

Step-by-step-explanation:

We have given that,

In figure, seg PQ || seg RS || seg TU.

Lines l and m are transversals.

• PR = 6

• RT = 3

• QS = 5

$\sf\:PQ\:\parallel\:RS\:\parallel\:TU\\\\\\\therefore\sf\:\dfrac{PR}{RT}\:=\:\dfrac{QS}{SU}\:\:\:-\:-\:[\:Property\:of\:three\:parallel\:lines\:\&\:their\:transversals\:]\\\\\\\implies\sf\:\cancel{\dfrac{6}{3}}\:=\:\dfrac{5}{SU}\\\\\\\implies\sf\:2\:=\:\dfrac{5}{SU}\\\\\\\implies\sf\:SU\:=\:\dfrac{\cancel5}{\cancel2}\\\\\\\implies\boxed{\red{\sf\:SU\:=\:2.5\:units}}$

Additional Information:

1. Parallel lines:

The lines which never intersect each other in a single point are called parallel lines.

2. Transversal:

A line which divides one single line or two parallel lines in two different points is called as a transversal.

3. Intercept:

When a transversal divides two or more parllalel lines in two or more different points, then the parts formed of the transversal are called as intercepts.

4. Property of three parallel lines and their transversals:

When two transversal divides three parallel lines in three different points, the intercepts formed on each of them are in the same ratio.