Geometry help?

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3 Answers
Mar 30, 2018

#x=16 2/3#

Explanation:

#triangleMOP# is similar to #triangleMLN# because all the angles of both triangles are equal.
This means that the ratio of two sides in one triangle will be same as that of another triangle so #"MO"/"MP"="ML"/"MN"#
After putting in values, we get #x/15=(x+20)/(15+18#

#x/15=(x+20)/33#

#33x=15x+300#

#18x=300#

#x=16 2/3#

Mar 30, 2018

#C#

Explanation:

We can use the Side-Splitter Theorem to solve this problem. It states:

  • If a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.

Since #OP# || #LN#, this theorem applies.

So we can set up this proportion:
#x/20 = 15/18#

Now cross multiply and solve:
#x/20 = 15/18#

#x xx 18 = 20 xx 15#

#18x = 300#

#x = 300/18 rarr 16 12/18 rarr 16 2/3#

So the answer is #C#

Mar 30, 2018

Answer: #x=16*2/3#

Explanation:

Since #OP# is parallel to #LN#, we know that #angleMOP=angleMLN# and #angleMPO=angleMNL# from the Corresponding Angles Theorem

Further, we also have that #angleOMP=angleLMN# since they are the same angle.

Therefore #triangleOMP# is similar to #triangleLMN# (#triangleOMP~triangleLMN#)

Since similar triangles have the same side length ratio:
#(MO)/(ML)=(MP)/(MN)#

Plugging numbers in, we have:
#x/(x+20)=15/(15+18)#

We can now solve this equation by cross multiplication:
#33x=15(x+20)#
#33x=15x+300#
#18x=300#
#x=16*2/3#