Question

in the diagram below of triangle NPQ, R is a midpoint of NP and S is a midpoint of PQ. If RS = 47 - 5x, and NQ = 5x - 11, what is the measure of RS?​

Answer 1

Answer:

Therefore the measure of RS is 12 unit.

Step-by-step explanation:

Given:

In ΔNPQ,

R is a midpoint of NP and

S is a midpoint of PQ.  

RS = 47 - 5x, and NQ = 5x - 11

To Find:

RS = ?

Solution:

Mid Point Theorem:

The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is equal to one half of the third side.

Here ,R is a midpoint of NP and

          S is a midpoint of PQ.  

∴ $RS=\dfrac{1}{2}NQ$

Substituting the values we get

$47-5x=\dfrac{1}{2}(5x-11)\\\\2(47-5x)=5x-11\\\\94-10x=5x-11\\5x+10x=94+11\\15x=105\\x=\dfrac{105}{15}=7\\x=7$

Now Substituting ' x ' in RS we get

$RS=47-5\times 7=47-35=12\\RS=12\ unit$

Therefore the measure of RS is 12 unit.