A triangle on a coordinated plane was dilated. After being dilated, its area is 6.25 times as the original figure. What was the scale factor?

Answer 1

Let's call the scale factor of the dilation $k$. Since area is a two-dimensional measurement, it scales with area squared.

If $A$ is the area of the original triangle and $A'$ is the area of the dilated triangle, we have the equation $A' = k^2 \cdot A$.

We are given that $A' = 6.25 \cdot A$. Substituting into the equation, we have $6.25 \cdot A = k^2 \cdot A$.

Canceling out the $A$, we get $6.25 = k^2$.

Taking the square root of both sides, we find $k = \sqrt{6.25}$.

Taking the square root, we find that $k = \boxed{2.5}$.