Respuesta :

tdpuppies14
Knowing that similar polygons have sides in proportion we can set up a scale factor between the small rectangle and large rectangle. This is basically a ratio of one side of the small rectangle and the corresponding side of the larger rectangle.

scale factor: 4/6 = 2/3
Therefore all sides on the smaller rectangle and all corresponding sides on the larger rectangle are in the proportion 2/3. 

We can apply this formula to find TU. 

2/3 = 10/TU
Cross multiply as always
2TU=30
TU = 15
boffeemadrid

Answer:

15 units

Step-by-step explanation:

It is given that the rectangle MNOP is similar to rectangle STUV, therefore applying the proportionality theorem, we get

[tex]\frac{NO}{TU}=\frac{OP}{UV}[/tex]

⇒[tex]\frac{10}{x}=\frac{4}{6}[/tex]

⇒[tex]x=\frac{10{\times}6}{4}[/tex]

⇒[tex]x=\frac{60}{4}[/tex]

⇒[tex]x=15[/tex]

Thus, the length of TU will be 15 units.

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