Triangle Q R S is cut by line segment V W. Point V is the midpoint of side Q S and point W is the midpoint of side R S. The length of Q R is 3 a + 6, the length of V W is 2 a minus 2, and the length of V S is 2 a. If V is the midpoint of Line segment Q S and W is the midpoint of Line segment R S, then what is VS?

4 units
8 units
10 units
20 units

20 units

Step-by-step explanation:

We can see that triangle QRS and triangle VWS are similar triangles.

Similar triangles are triangles in which the ratio of their corresponding sides are in the same proportion.

V is the midpoint of QS.

VS = 2a, QS = 2 * VS = 2(2a) = 4a

Since both triangles are similar triangles, hence:

\begin{gathered}\frac{VS}{QS}=\frac{VW}{QR}frac{2a}{4a} =\frac{2a-2}{3a+6} frac{2a-2}{3a+6} =\frac{1}{2} 2(2a-2)=3a+64a-4=3a+6a=10\ unitsVS=2a=2(10)=20\ units\end{gathered}

QS

VS

=

QR

VW

4a

2a

=

3a+6

2a−2

3a+6

2a−2

=

2

1

2(2a−2)=3a+6

4a−4=3a+6

a=10 units

VS=2a=2(10)=20 units

ur wlcm♥️♥️

20 UNITS

Step-by-step explanation:

EDG 2020

8

step-by-step explanation:

b.

step-by-step explanation: