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

Answer:

$TU = 15$

Step-by-step 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

$\frac{10 }{ 4 } = \frac{x }{ 6}$

Multiply both sides by 6

$6 * \frac{10 }{ 4 } = \frac{x }{ 6} * 6$

$6 * \frac{10 }{ 4 } = x$

$x = 6 * \frac{10 }{ 4 }$

$x = \frac{60 }{ 4 }$

$x = 15$

Hence:

$TU = 15$