+0

0
414
1

What is the value of x?

?cm

http://prntscr.com/i1bhk7

(I just added the pic - Melody)

Jan 16, 2018
edited by Guest  Jan 16, 2018
edited by Melody  Jan 16, 2018

#1
+2338
+1

$$\triangle MNP\sim\triangle MAB$$ because a segment located in the interior of the triangle is parallel to a side. You could also prove similarity by Angle-Angle Similarity Theorem.

Using the above similarity statement, one can create a proportion because each side is proportional. The one I will use is $$\frac{MA}{MB}=\frac{MN}{MP}$$. This comes from the similarity statement.

Although we do not know the length of $$\overline{MA}$$ directly, we can find it by subtracting the length of $$\overline{AN}$$ from the length of $$\overline{MN}$$. When we plug in these numbers, we can then solve for the unknown side length.

 $$\frac{MA}{MB}=\frac{MN}{MP}$$ Plug in the known information and solve for the unknown. $$\frac{46.2-14}{x}=\frac{46.2}{72.6}$$ Let's simplify the numerator of the left hand side of the equation first. $$\frac{32.2}{x}=\frac{46.2}{72.6}$$ Before proceeding, it may be wise to multiply the fractions by 10/10 so that the numbers are whole numbers. $$\frac{322}{10x}=\frac{462}{726}$$ Some simplification can occur here. The numerator and denominator of the right hand side happen to have a greatest common factor of 66. That's something you don't see every day! $$\frac{161}{5x}=\frac{7}{11}$$ Now, let's do the cross multiplication with simplified numbers. $$1771=35x$$ Divide by 35 from both sides. $$x=\frac{1771}{35}=\frac{253}{5}=50.6$$
Jan 17, 2018

#1
+2338
+1

$$\triangle MNP\sim\triangle MAB$$ because a segment located in the interior of the triangle is parallel to a side. You could also prove similarity by Angle-Angle Similarity Theorem.

Using the above similarity statement, one can create a proportion because each side is proportional. The one I will use is $$\frac{MA}{MB}=\frac{MN}{MP}$$. This comes from the similarity statement.

Although we do not know the length of $$\overline{MA}$$ directly, we can find it by subtracting the length of $$\overline{AN}$$ from the length of $$\overline{MN}$$. When we plug in these numbers, we can then solve for the unknown side length.

 $$\frac{MA}{MB}=\frac{MN}{MP}$$ Plug in the known information and solve for the unknown. $$\frac{46.2-14}{x}=\frac{46.2}{72.6}$$ Let's simplify the numerator of the left hand side of the equation first. $$\frac{32.2}{x}=\frac{46.2}{72.6}$$ Before proceeding, it may be wise to multiply the fractions by 10/10 so that the numbers are whole numbers. $$\frac{322}{10x}=\frac{462}{726}$$ Some simplification can occur here. The numerator and denominator of the right hand side happen to have a greatest common factor of 66. That's something you don't see every day! $$\frac{161}{5x}=\frac{7}{11}$$ Now, let's do the cross multiplication with simplified numbers. $$1771=35x$$ Divide by 35 from both sides. $$x=\frac{1771}{35}=\frac{253}{5}=50.6$$
TheXSquaredFactor Jan 17, 2018