Question

PLEASE HELP!!!!

An architect is planning to make two triangular prisms out of iron.

The architect will use ∆ABC for the bases of one prism and ∆DEF for the bases of the other prism.


What is the scale factor from ∆ABC to ∆DEF?





Suppose the height of the prism made by ∆ABC is 15 inches. What is the volume of the prism made by ∆ABC?


Suppose the volume of the prism made by ∆ABC is 4459 〖"in" 〗^3.

What is the volume of the prism made by ∆DEF?

Answer 1

Part A:

In triangle ABC and DEF,

`\begin{aligned}&(A B)/(D E)=(28)/(20)=(7)/(5)\\&(B C)/(E F)=(21)/(25)=(7)/(5)\\\end{aligned}`

If the ratios of lengths of the sides of two triangles are same, then the triangles are similar.

Therefore ΔABC
`\sim` ΔDEF.

Scale factor of two triangles =
`(7)/(5)`

Part B:

Suppose height of the prism made by ΔABC = 15 inches

Volume of the prism made by ΔABC = Area of the triangle × height

`=(1)/(2)*21*28*15`

= 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 =
`((7)/(5) )^2` × volume of the smaller triangle

`\Rightarrow 4459=((49)/(25) )` × volume of the smaller triangle

`\Rightarrow 4459* ((25)/(49) )=` volume of the smaller triangle

Volume of the smaller triangle ΔDEF = 2275 inch³