Respuesta :

semsee45

Answer:

ST = 63

HI = 28

IJ = 21

Step-by-step explanation:

Given:  RSTUV ~ JFGHI

From inspection of the diagram, the corresponding sides are:

RS~JF

ST~FG

TU~GH

UV~HI

VR~IJ

The only pair of sides that both have side lengths are TU and GH. Therefore, we can use these to figure out the scale factor of dilation.

TU = 72   and   GH = 56

⇒ TU/GH = 72/56 = 9/7

Therefore, RSTUV is an enlargement of JFGHI by a scale factor of 9/7

If FG = 49

⇒ ST = 49 × 9/7 = 63

If UV = 36

⇒ HI = 36 ÷ 9/7 = 28

If VR = 27

⇒ IJ = 27 ÷ 9/7 = 21

igoroleshko156

Answer:

ST = 63, HI = 28, IJ = 21

Step-by-step explanation:

Step 1:  Determine the scale

UT = 72 and HG = 56

[tex]72 / 56 = 9/7[/tex]

Step 2:  Determine ST

We can determine ST by multipliying GF by 9/7 which will give us the upscaled ratio which will produce ST.

[tex]ST = GF * 9/7[/tex]

[tex]ST = 49 * 9/7[/tex]

[tex]ST = 63[/tex]

Step 3:  Determine HI

We can determine ST by dividng VU by 9/7 which will give us the upscaled ratio which will produce ST.

[tex]HI = VU / (9/7)[/tex]

[tex]HI = 36 / (9/7)[/tex]

[tex]HI = 28[/tex]

Step 4:  Determine IJ

We can determine IJ by dividng RV by 9/7 which will give us the upscaled ratio which will produce IJ.

[tex]IJ = RV / (9/7)[/tex]

[tex]IJ = 27 / (9/7)[/tex]

[tex]IJ = 21[/tex]

Answer: ST = 63, HI = 28, IJ = 21

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