Question

the scale factor of triangle a to triangle b is 1:4\frac{5}{8}. what is the value of x? x = enter answer

Explanation:

Step1: Understand Scale Factor

The scale factor from Triangle A to Triangle B is \(1:4\frac{5}{8}\). First, convert the mixed number \(4\frac{5}{8}\) to an improper fraction. \(4\frac{5}{8}=\frac{4\times8 + 5}{8}=\frac{37}{8}\).

Step2: Set Up Proportion

Since the triangles are similar (scale factor given), the ratio of corresponding sides is equal to the scale factor. The side of Triangle A is 5, and the corresponding side of Triangle B is \(x\). So, \(\frac{5}{x}=\frac{1}{\frac{37}{8}}\) (or equivalently, \(x = 5\times\frac{37}{8}\)).

Step3: Calculate \(x\)

Multiply 5 by \(\frac{37}{8}\): \(5\times\frac{37}{8}=\frac{185}{8}\). Convert \(\frac{185}{8}\) to a mixed number: \(\frac{185}{8}=23\frac{1}{8}\) (or as a decimal, 23.125).

Answer:

\(23\frac{1}{8}\) (or \(23.125\) or \(\frac{185}{8}\))