Question

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

Answer 1

(1)

we are given

U is the midpoint of RS

and we have

$RU=12$

so, we can use formula

$RS=2RU$

we can plug values

$RS=2\times 12$

$RS=24$............Answer

(2)

V is the midpoint of ST

so, we get

$SV=VT$

now, we can plug values

$2x=11$

divide both sides by 2

$x=5.5$.........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

$RW=WT$

we can plug value

$15.9=3y$

divide both sides by 3

$y=5.3$

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

$\frac{RW}{RT} =\frac{UW}{ST}$

we can plug values

$\frac{15.9}{2\times 15.9} =\frac{UW}{2VT}$

$\frac{15.9}{2\times 15.9} =\frac{UW}{2\times 11}$

$UW=22\times \frac{15.9}{2\times 15.9}$

$UW=11$...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

$\frac{SU}{SR} =\frac{UV}{RT}$

now, we can plug values

$\frac{12}{2\times 12} =\frac{UV}{2\times 15.9}$

$UV=2\times 15.9\times \frac{12}{2\times 12}$

$UV=15.9$.............Answer