Question

Given that rectangle MNOP ~ rectangle STUV, what is the length of ¯¯¯¯¯¯ T U ?Rectangle M N O P is shown with segment N O labeled 10 and segment O P labeled 4. rectangle S T U V is shown with segment T U labeled x and segment U V labeled 6

Answer 1

`TU = 15`

Explanation:

Given

`\square MNOP \simeq\ \square STUV`

`NO = 10`

`OP = 4`

`TU = x`

`UV = 6`

Required

Determine the length of TU (i.e. x)

Because both shapes are similar, then the following equivalent ratios exist:

`NO : OP = TU : UV`

Substitute values for NO, OP, TU and UV

`10 : 4 = x : 6`

Represent as fraction

`(10 )/( 4 ) = (x )/( 6)`

Multiply both sides by 6

`6 * (10 )/( 4 ) = (x )/( 6) * 6`

`6 * (10 )/( 4 ) = x`

`x = 6 * (10 )/( 4 )`

`x = (60 )/( 4 )`

`x = 15`

Hence:

`TU = 15`