In the diagram the length of segment tr can be represented by 5x-4.
what is the length os vs?
a) 3 units
b) 11 units
c) 13 units
d) 15 units

The correct option is D, i.e., 15 units.

Explanation:

It is given that the  length of segment TR can be represented by 5x-4.

From figure it is noticed that the side TR and RV is equal and the length of segment RV is 2x+5. So,

The value of x is 3, so the length of side RV is,

In triangle TRS and angle VRS,

TR=VR

RS=RS (common side)

By SAS rule of congruence triangle,

Therefore the side TS and VS are congruent sides.

From figure it is noticed that the length of side TS is 6x-3, therefore the length of side VS is also 6x-3.

Hence, the length of side VS is 15 units and option D is correct.

Step

Find the value of x

we know that

TR=RV -------> given problem

in this problem we have

so

Step

In the right triangle TRS

Find the length of the side RS

we know that

Applying the Pythagorean Theorem

in this problem we have

Substitute the value of x

Step

In the right triangle RSV

Find the length of the side VS

Applying the Pythagorean Theorem

in this problem we have

Substitute in the formula

therefore

the answer is the option D

the value of the side VS is

65

step-by-step explanation: