Question

A triangle with an area of 8 in^2 is dilated by a factor of 3.The area of the dilated triangle is ____ in^2.

Answer 1

Let x be the area of the dilated triangle

The ratio of the area of the image to the area of the pre-image is equal to the square of the scale factor

Let k be the scale factor

$\frac{\operatorname{Im}age\text{ area}}{\text{Pre image area}}=k^2$

From the question, k = 3 and pre image area = 8

substitute into the formula and evaluate

$\frac{x}{8}=3^2$

Multiply both-side by 8

$x=9\times8$$x=72in^2$

Hence, the area of the dilated triangle is 72 in²