Question

Rectangle $LOSP$ is shown. The lengths in units of some of the line segment are also shown. Line segments $MQ$ and $NR$ are perpendicular to the line segment $LO$Which shape is similar to rectangle $LOSP$?

• A. $LMQP$
• B. $LNRP$
• C. $MNRQ$
• D. $OSRN$

Answer 1

The correct option is D $OSRN$

Given, $LMOS$ is rectangle and $MQ$ and $NR$ are perpendicular to $LO$

Since, $LMOS$ is rectangle

$\Rightarrow$ $OS$ and $LP$ is perpendicular to $LO$ and $PS$

$\Rightarrow$ $MQ$ and $NP$ is also perpendicular

Now,

$LO=4+6+8=18$ (Length)

$OS=12$ (Breadth)

$\frac{LO}{OS}=\frac{18}{12}=\frac{3}{2}=\frac{Length}{Breadth}$

Now, $OSRN$ rectangle

$OS=12$ (length)

$NO=8$ (breadth)

$\frac{length}{breadth}=\frac{12}{8}=\frac{3}{2}$

$\Rightarrow OSRN$ rectangle is similar to $LOSP$ rectangle