The two triangles, ABC and FGH are congruent.
The length of two corresponding sides are given,
[tex]\begin{gathered} \text{If }\Delta ABC\cong\Delta FGH \\ \text{Then,} \\ AB\cong FG \\ \text{If AB=15, and FG=10} \\ \text{Then} \\ \text{Ratio}=\frac{FG}{AB} \\ \text{Ratio}=\frac{2}{3} \end{gathered}[/tex]
If the ratio of the sides is determined as 2/3, then the perimeter which is an addition of all three sides shall be;
[tex]\begin{gathered} AB=15 \\ FG=\frac{2}{3}\times15 \\ \text{Similarly,} \\ \text{Perimeter }\Delta ABC=36 \\ \text{Perimeter }\Delta FGH=\frac{2}{3}\times36 \\ \text{Perimeter }\Delta FGH=24in \end{gathered}[/tex]
To determine the area, we shall apply the ratio raied to the power of 2 (becaue the area i in units squared).
Therefore, we would have;
[tex]\begin{gathered} \text{Area }\Delta ABC=45in^2 \\ \text{Area }\Delta FGH=45\times(\frac{2}{3})^2 \\ \text{Area }\Delta FGH=45\times\frac{4}{9} \\ \text{Area }\Delta FGH=20in^2 \end{gathered}[/tex]
Therefore, the perimeter of triangle FGH is 24 inches
The area of triangle FGH is 20 inches squared
