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

Given that line segments MQ and NR are perpendicular to line segment LO, the shape that is similar to rectangle LOSP is d. MNRQ.

How to determine which shape is similar to rectangle LOSP

To determine which shape is similar to rectangle LOSP, consider the relationships between the line segments and the right angles.

In rectangle LOSP, we know that line segments MQ and NR are perpendicular to line segment LO.

In a rectangle, opposite sides are parallel and equal in length, and all angles are right angles.

Given the information that line segments MQ and NR are perpendicular to line segment LO within the rectangle LOSP, the shape that would be similar to the rectangle LOSP is the one formed by MQ and NR.

Therefore, the shape that is similar to rectangle LOSP is

d.MNRQ.

Answer 2

Answer: c. OSRN

Explanation:

Sides of similar shapes are proportional.

For Rectangle LOSP,

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

Width = OS= 12 units

Here,
`(18)/(12)=(3)/(2)` [proportionality constant]

a. For Rectangle LMQP,

Length = MQ = 12 units

Width = LM = 4 units

Here,
`(12)/(4)=3\\eq\frac32`

LMQP is not similar to LOSP.

b. Similarly, for LNRP,

Width = LN= 4+6 = 10

length = NR = 12

`(12)/(10)\\eq\frac32`

LNRP is not similar to LOSP.

c. For OSRN,

Length = OS = 12

Width = ON = 8

`(12)/(8)=\frac32`

OSRN is similar to LOSP.

d. For MNRQ,

Length= NR = 12

Width = MN = 6

`(12)/(6)=2\\eq\frac32`

MNRQ is not similar to LOSP.

Hence, the shape similar to rectangle LOSP is OSRN.