Respuesta :
Given data:
The side of the first triangle is x= 12 meter.
The side of the second triangle is y=8 meter.
The perimeter of the first triangle is P= 48 meter.
The expression for the ratio of the similar triangle,
[tex]\begin{gathered} \frac{x}{y}=\frac{P}{p} \\ \frac{12\text{ m}}{8\text{ m}}=\frac{48\text{ m}}{p} \\ p=48\text{ m(}\frac{8}{12}) \\ =32\text{ m} \end{gathered}[/tex]The expression for the area is,
[tex]\begin{gathered} \frac{x^2}{y^2}=\frac{A}{a} \\ \frac{(12m)^2}{(8m)^2}=\frac{180m^2}{a} \\ a=\frac{1}{2.25}\times180m^2 \\ =80m^2 \end{gathered}[/tex]Thus, the perimeter of the smaller triangle is 32 m, and the area of the smaller triangle is 80 square-meter.
