Answer:
Therefore the true statement is that the height of the red prism is three times the height of the blue prism.
Step-by-step explanation:
i) Volume of blue prism = (base of blue prism) [tex]\times[/tex] (height of blue prism)
ii) base of red prism = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (base of blue prism)
iii) Volume of red prism = (base of red prism) [tex]\times[/tex] (height of red prism)
= [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (base of blue prism) [tex]\times[/tex] (height of red prism)
iv) Volume of blue prism = Volume of red prism
∴ (base of blue prism) [tex]\times[/tex] (height of blue prism) = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (base of blue prism) [tex]\times[/tex] (height of red prism)
∴height of blue prism = [tex]\frac{1}{3}[/tex] [tex]\times[/tex] (height of red prism)
Therefore the true statement is that the height of the red prism is three times the height of the blue prism.