What is the value of x?
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?cm
(I just added the pic - Melody)
+2441 \(\triangle MNP\sim\triangle MAB\) 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. |
| \(x=\frac{1771}{35}=\frac{253}{5}=50.6\) | |
+2441 \(\triangle MNP\sim\triangle MAB\) 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. |
| \(x=\frac{1771}{35}=\frac{253}{5}=50.6\) | |
