Question

Rectangle LOSP is shown below. The lengths, in units, of some of the line segments are also shown. Line segments MQ and NR are perpendicular to line segment LO. Which shape is similar to rectangle LOSP?
Select one:
a. LMQP
b. LNRP
c. OSRN
d. MNRQ

Answer 1

Answer: c. OSRN

Step-by-step explanation:

Sides of similar shapes are proportional.

For Rectangle LOSP,

Length = LO = 4+6+8 = 18 units

Width = OS= 12 units

Here, $\dfrac{18}{12}=\dfrac{3}{2}$  [proportionality constant]

a. For Rectangle LMQP,

Length = MQ = 12 units

Width = LM = 4 units

Here, $\dfrac{12}{4}=3\neq\dfrac32$

LMQP is not similar to LOSP.

b. Similarly, for LNRP,

Width = LN= 4+6 = 10

length = NR = 12

$\dfrac{12}{10}\neq\dfrac32$

LNRP is not similar to LOSP.

c. For OSRN,

Length = OS = 12

Width = ON = 8

$\dfrac{12}{8}=\dfrac32$

OSRN is similar to LOSP.

d. For MNRQ,

Length= NR = 12

Width = MN = 6

$\dfrac{12}{6}=2\neq\dfrac32$

MNRQ  is not similar to LOSP.

Hence, the shape similar to rectangle LOSP is OSRN.