Question

the right triangle below is the image of a right triangle that was dilated by a scale factor of 3. find the area of the preimage, the original right triangle, before its dilation. figures are not necessarily drawn to scale.

Explanation:

Step1: Find preimage legs

Dilation scale factor \( k = 3 \). For a right triangle, legs of preimage are \( \frac{72}{3} \) and \( \frac{21}{3} \).
\( \frac{72}{3} = 24 \), \( \frac{21}{3} = 7 \).

Step2: Calculate preimage area

Area of right triangle: \( \frac{1}{2} \times \text{base} \times \text{height} \).
Substitute base \( = 24 \), height \( = 7 \):
\( \frac{1}{2} \times 24 \times 7 = 12 \times 7 = 84 \).

Answer:

84