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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

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 class=

Respuesta :

(1)

we are given

U is the midpoint of RS

and we have

[tex]RU=12[/tex]

so, we can use formula

[tex]RS=2RU[/tex]

we can plug values

[tex]RS=2\times 12[/tex]

[tex]RS=24[/tex]............Answer

(2)

V is the midpoint of ST

so, we get

[tex]SV=VT[/tex]

now, we can plug values

[tex]2x=11[/tex]

divide both sides by 2

[tex]x=5.5[/tex].........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

[tex]RW=WT[/tex]

we can plug value

[tex]15.9=3y[/tex]

divide both sides by 3

[tex]y=5.3[/tex]

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

[tex]\frac{RW}{RT} =\frac{UW}{ST}[/tex]

we can plug values

[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2VT}[/tex]

[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2\times 11}[/tex]

[tex]UW=22\times \frac{15.9}{2\times 15.9}[/tex]

[tex]UW=11[/tex]...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

[tex]\frac{SU}{SR} =\frac{UV}{RT}[/tex]

now, we can plug values

[tex]\frac{12}{2\times 12} =\frac{UV}{2\times 15.9}[/tex]

[tex]UV=2\times 15.9\times \frac{12}{2\times 12}[/tex]

[tex]UV=15.9[/tex].............Answer

ernikhil

1. The length of RS is 24 units.

2. The value of [tex]x[/tex] is 5.5.

3. The value of [tex]y[/tex] is 5.3.

4. The length of UW is 11.

5. The length of UV is 15.9.

According to the given figure-

[tex]\triangle RST \sim \triangle URW[/tex]

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,

[tex]2x=11\\x=\dfrac{11}{2}\\x=5.5[/tex]

Hence, the value of [tex]x[/tex] is 5.5.

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

So,

[tex]3y=15.9\\y=\dfrac{15.9}{3}\\y=5.3[/tex]

Hence, the value of [tex]y[/tex] is 5.3.

4. As, [tex]\triangle RST \sim \triangle URW[/tex]

So, the length of the sides is proportional.

[tex]\dfrac{RT}{RW}=\dfrac{ST}{UW}\\\dfrac{2\times 15.9}{15.9}=\dfrac{11\times 2}{UW}\\UW=11[/tex]

Hence, the length of UW is 11.

5.  As, [tex]\triangle RST \sim \triangle URW[/tex]

So, the length of the sides is proportional.

[tex]\dfrac{SU}{SR}=\dfrac{UV}{RT}\\\dfrac{12}{2\times 12}=\dfrac{UV}{2\times 15.9}\\UV=15.9[/tex]

Hence, the length of UV is 15.9.

Learn more about similar triangles here:

https://brainly.com/question/20502277?referrer=searchResults

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