In triangle rst, u is the midpoint of rs, v is the midpoint of st, and w is the midpoint of tr. use the triangle diagram to answer the question. 1. what is the length of 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 uw? a. 11 b. 6 c. 7.95 d. 22 5. what is the length of uv? a. 11 b. 6 c. 7.95 d. 12

(1)

we are given

U is the midpoint of RS

and we have

so, we can use formula

we can plug values

............Answer

(2)

V is the midpoint of ST

so, we get

now, we can plug values

divide both sides by 2

.........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

we can plug value

divide both sides by 3

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

we can plug values

...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

now, we can plug values

.............Answer

1. The length of RS is 24 units.

2. The value of is 5.5.

3. The value of is 5.3.

4. The length of UW is 11.

5. The length of UV is 15.9.

According to the given figure-

1. U is the mid-point of RS so, the length of UR and US are equal.

Hence, the length of RS is 24 units.

2. V is the mid-point of ST so, the length of VS and VT are equal.

So,

Hence, the value of is 5.5.

3. W is the mid-point of RT so, the length of WR and WT are equal.

So,

Hence, the value of is 5.3.

4. As,

So, the length of the sides is proportional.

Hence, the length of UW is 11.

5.  As,

So, the length of the sides is proportional.

Hence, the length of UV is 15.9.

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