Question

Each side of a triangle is multiplied by 3. How will thearea change?The area of the new triangle will be 1.5times the area of the first triangle.The area of the new triangle will be 3times the area of the first triangle.The area of the new triangle will be 6times the area of the first triangle.The area of the new triangle will be 9times the area of the first triangle.

Answer 1

From a generic triangle:

Once you multiply every side by 3, also the height will be multiplied by 3. The triangle's area is given by the base multiplied by the height and divided by 2. From this generic definition, we can write as it follows:

For the first triangle:

$A_1=\frac{h\times c}{2}$

And for the second, that is the first stretched:

$\begin{gathered} A_2=\frac{3h\times3c}{2}=3\times3\times\frac{h\times c}{2} \\ A_2=9\times A_1 \end{gathered}$

From this, we can assume that the area of the original triangle was multiplied by 9. And the correct answer for the present question is the fourth option:

The area of the new triangle will be 9 times the area of the first triangle.