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 below are not drawn to scale.)

Explanation:

Step1: Recall scale factor effect

When a figure is scaled by a factor \( k \), all linear dimensions (like height, base) are multiplied by \( k \). Here, scale factor \( k=\frac{1}{4} \).

Step2: Calculate scaled height

Original height \( H = 16 \) cm. Scaled height \( h=H\times k = 16\times\frac{1}{4}=4 \) cm.

Step3: Calculate scaled base

Original base \( B = 12 \) cm. Scaled base \( b = B\times k=12\times\frac{1}{4} = 3 \) cm.

Looking at the options, the triangle with height 4 cm and base 3 cm matches.

Answer:

The triangle with 4 cm (height) and 3 cm (base) (the first option in the given choices: 4 cm height, 3 cm base).