Question

which scale drawing of a triangle was created by using a scale factor of \\( \frac { 1 } { 4 } \\), if the original right triangle has a height of 16 cm and a base length of 12 cm? (the figures are not drawn to scale.)

Explanation:

Step1: Calculate the scaled - down base length

The formula for the scale factor \(k\) is \(k=\frac{\text{scaled length}}{\text{original length}}\). Given \(k = \frac{1}{4}\) and the original base length \(b_{original}=12\space cm\).
We use the formula \(b_{scaled}=k\times b_{original}\).
Substitute \(k=\frac{1}{4}\) and \(b_{original} = 12\) into the formula: \(b_{scaled}=\frac{1}{4}\times12\).

$$ \frac{1}{4}\times12=\frac{12}{4}=3 $$

Step2: Calculate the scaled - down height

The original height \(h_{original}=16\space cm\). Using the scale factor formula \(h_{scaled}=k\times h_{original}\).
Substitute \(k = \frac{1}{4}\) and \(h_{original}=16\) into the formula: \(h_{scaled}=\frac{1}{4}\times16\).

$$ \frac{1}{4}\times16=\frac{16}{4} = 4 $$

Answer:

The triangle with base \(3\space cm\) and height \(4\space cm\) (the third triangle in the image) is the scale drawing.