We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

What is the value of x?

Enter your answer, as a decimal, in the box.

?cm

(I just added the pic - Melody)

Guest Jan 16, 2018

#1**+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

#1**+1 **

Best Answer

\(\triangle MNP\sim\triangle MAB\) 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