Question

PLEASE HELP QUICK QUESTION EARN 20 POINTS

Which value of y would make OP || LN?

16
24
32
36

Answer 1

Option D. y= 36

Explanation:

In the given figure there are two triangles ΔMPO and ΔMNL

If two sides OP and LN are parallel and lines MN, ML are transverse respectively.

Then ∠MPO =∠MNL [ corresponding angles ]

and ∠MOP = ∠MLN [ corresponding angles ]

and ∠M is common to both the triangles.

Now by the property of AAA, ΔMPO & ΔMNL are similar

Now we know in similar triangles corresponding sides are in same ratio.

`(MP)/(MN)=(MO)/(ML)`

`(y)/(y+18)=(28)/(28+14)=(28)/(42)=(2)/(3)`

By cross multiplication

3y = 2(y + 18)

3y = 2y + 36

y = 36

Option D. y = 36 is the answer.

Answer 2

Answer: The correct option is (D) 36.

Step-by-step explanation: We are given to find the value of 'y' that would make OP parallel to LN.

MO = 28 units, OL= 14 units, Pl = 18 units and MP = y = ?

From the figure, we have

if OP ║ LN, then we must have

∠MOP = ∠MLN

and

∠MPO = ∠MNL.

Since ∠M is common to both the triangles MOP and MLN, so by AAA postulate, we get

ΔMOP similar to ΔMLN.

We know that the corresponding sides of two similar triangles are proportional, so

`(MO)/(ML)=(MP)/(MN)\\\\\\\Rightarrow (MO)/(MO+OL)=(MP)/(MP+PN)\\\\\\\Rightarrow (28)/(28+14)=(y)/(y+18)\\\\\\\Rightarrow (28)/(42)=(y)/(y+18)\\\\\\\Rightarrow (2)/(3)=(y)/(y+18)\\\\\\\Rightarrow 2y+36=3y\\\\\Rightarrow y=36.`

Thus, the required value of 'y' is 36.

(D) is the correct option.