The sides of the given triangle are 15,20 and 25.
[tex]\begin{gathered} \text{Perimeter of the triangle =15+20+25} \\ =60 \end{gathered}[/tex]
Find the area.
[tex]\begin{gathered} A\text{rea of the triangle =}\frac{1}{2}\cdot15\cdot20 \\ =150 \end{gathered}[/tex]
The length of the sides of the dilated triangle are 3 times the sides of the original triange.
So, the sides of the dilated triangle are:
[tex]\begin{gathered} 15\cdot3=45 \\ 20\cdot3=60 \\ 25\cdot3=75 \end{gathered}[/tex]
So, the perimeter of the dilated triangle is the sum of 45, 60 and 75.
[tex]\begin{gathered} \text{Perimeter of the dilated triangle=45+60+75} \\ =180 \end{gathered}[/tex]
Now, find the area of the dilated triangle.
[tex]\begin{gathered} \text{Area of the dilated triangle =}\frac{1}{2}\cdot45\cdot60 \\ =1350 \end{gathered}[/tex]
