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Xelga [282]
2 years ago
14

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 answ

er 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

Mathematics
1 answer:
Zolol [24]2 years ago
4 0

(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

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