Part A:
In triangle ABC and DEF,
[tex]\begin{aligned}&\frac{A B}{D E}=\frac{28}{20}=\frac{7}{5}\\&\frac{B C}{E F}=\frac{21}{25}=\frac{7}{5}\\\end{aligned}[/tex]
If the ratios of lengths of the sides of two triangles are same, then the triangles are similar.
Therefore ΔABC [tex]\sim[/tex] ΔDEF.
Scale factor of two triangles = [tex]\frac{7}{5}[/tex]
Part B:
Suppose height of the prism made by ΔABC = 15 inches
Volume of the prism made by ΔABC = Area of the triangle × height
[tex]=\frac{1}{2}\times21\times28\times15[/tex]
= 4410 inch³
Volume of the prism made by ΔABC = 4410 inch³
Part C: Suppose the volume of the prism made by ΔABC = 4459 inch³
Volume of the larger prism = (Scale factor)² × volume of the smaller triangle
Volume of the larger prism = [tex](\frac{7}{5} )^2[/tex] × volume of the smaller triangle
[tex]\Rightarrow 4459=(\frac{49}{25} )[/tex] × volume of the smaller triangle
[tex]\Rightarrow 4459\times (\frac{25}{49} )=[/tex] volume of the smaller triangle
Volume of the smaller triangle ΔDEF = 2275 inch³
