Please show work i would appreciate it

a) x = 14

b) The perimeter of △QRS is 77 units.

Step-by-step explanation:

a) Due to the question asking for a solution using the Triangle Proportionality Theorem, it is assumed that △RQS is similar to the smaller triangle inside it.

Let us define the point at which the line inside △RQS meets line RQ as T, and the point at which that same line meets line RS as V.

Hence, △RTV ~ △RQS.

According to the Triangle Proportionality Theorem:

Hence, we can substitute all values that we know from the diagram:

After getting this information, all we have to do is simplify and solve the equation:

To verify this answer, we can plug in the value of x into the equation:

Hence, after verification, we can get the x = 14.

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b) To find the perimeter of △QRS, all we have to do is to add all the lengths of the sides of △QRS together.

Hence, 2(14) - 2 + 13 + 17 + 21

= 28 - 2 + 13 + 17 + 21

= 77 units

Therefore, the perimeter of △QRS is 77 units.

Hope this helped!

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step-by-step explanation:

no friends = cant give anything out

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step-by-step explanation: