Question

Given that rectangle MNOP ~ rectangle STUV, what is the length of TU

Answer 1

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

$\frac{NO}{TU}=\frac{OP}{UV}$

⇒$\frac{10}{x}=\frac{4}{6}$

⇒$x=\frac{10{\times}6}{4}$

⇒$x=\frac{60}{4}$

⇒$x=15$

Thus, the length of TU will be 15 units.

Answer 2

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