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.
∴ [tex]RS=\dfrac{1}{2}NQ[/tex]
Substituting the values we get
[tex]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[/tex]
Now Substituting ' x ' in RS we get
[tex]RS=47-5\times 7=47-35=12\\RS=12\ unit[/tex]
Therefore the measure of RS is 12 unit.
