1. what is the length of line rs? a)12 b)6 c)22 d)24 2. what is the value of x? a) 6.5 b) 6 c) 11 d) 5.5 3. what is the value of y? a) 15.9 b) 11 c) 5.3 d) 3.7 4. what is the length of line uw? a) 11 b) 6 c) 7.95 d) 22 5. what is the length of line uv? a) 11 b) 7.95 c) 15.9 d) 12

1) The length of the side RS is 24 units. 2) The value of is 5.5 units. 3) The value of is 5.3 units. 4) The length of side UW is 11 units. 5) The length of side UV is 15.9 units.

Given information:

In triangle RST, U is the mid-point of side SR, V is the mid-point of the side ST and W is the mid-point of the side RT.

So, the length of the sides can be written as,

It is also given that:

1). Now, the length of side SR will be,

The length of the side RS is 24 units.

2). To find the value of , use the relation between SV and VT as,

The value of is 5.5 units.

3). To find the value of , use the relation between RW and WR as,

The value of is 5.3 units.

Now, the mid-point theorem states that "a line segment joining the mid-points of two sides of a triangle is parallel to the third side and its length is equal to half of the third side".

4). Use the mid-point theorem to get the value of side UW as,

Thus, the length of side UW is 11 units.

5). Use the mid-point theorem to get the value of side UV as,

Thus, the length of side UV is 15.9 units.

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