Question

All the dimensions of a triangle were multiplied by the same factor. If the base of the triangle went from 1 centimeter to 3 centimeters, the area of the triangle was multiplied by

Answer 1

The answer is 9.

To calculate this, we will use Galileo's square cube law, used to describe the change of the area or the volume of the shape, when their dimensions increase or decrease. The formula used for change of the area is
$A_2= A_1 (\frac{l_2}{l_1} )^{2}$
A₂ - the area after the change,
A₁ - the area before the change,
l₂ - the dimension after the change,
l₁ - the dimension before the change.


It is given:
l₁ = 1 cm
l₂ = 3 cm

Let's use this formula for the mentioned triangle:
$A_2=A_1( \frac{l_2}{l_1}) ^{2} =A_1( \frac{3}{1})^{2} =A_1*3 ^{2} =9A_1$

Therefore, the area of the triangle was multiplied by 9.