Question

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

Answer 1

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

Answer 2

15 units

Explanation:

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

`(NO)/(TU)=(OP)/(UV)`

⇒
`(10)/(x)=(4)/(6)`

⇒
`x=\frac{10{*}6}{4}`

⇒
`x=(60)/(4)`

⇒
`x=15`

Thus, the length of TU will be 15 units.