Question

triangle bcd is dilated by a scale factor of 3 to form triangle bcd. what is the measure of side db?

Explanation:

Step1: Recall the dilation formula

If a figure is dilated by a scale factor \(k\), the length of a side of the original figure \(x\) and the length of the corresponding side of the dilated figure \(y\) are related by \(y = kx\). Here, \(k = 3\), and we want to find \(x\) (the length of \(DB\)) given \(y\) (the length of \(D'B'\)) is \(84\).

Step2: Solve for \(x\)

Using the formula \(y=kx\), we can rewrite it as \(x=\frac{y}{k}\). Substitute \(y = 84\) and \(k = 3\) into the formula: \(x=\frac{84}{3}\).

$$x = 28$$

Answer:

\(28\)