The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism find the volume of each prism

The volume of the rectangular prism is 144 ft³.

The volume of the triangular prism is 112 ft³.

Step-by-step explanation:

For the rectangular prism:

Length (L) = 6 ft

Width (W) = x ft

Height (h) = 3 ft

Volume rectangular prism (Vr) =?

Vr = L × W × h

Vr = 6 × x × 3

Vr = 18x

For the triangular prism:

Length (L) = 7 ft

Base (b) = x ft

Height (h) = 4 ft

Volume of triangular prism (Vt) =?

Vt = ½bhL

Vt = ½ × x × 4 × 7

Vt = x × 2 × 7

Vt = 14x

From the question given above,

Volume of rectangular prism (Vr) is 32 cubic feet more than the volume of the right triangular prism (Vt).

This can be written as:

Vr = 32 + Vt

But:

Vr = 18x

Vt = 14x

Therefore,

Vr = 32 + Vt

18x = 32 + 14x

Collect like terms

18x – 14x = 32

4x = 32

Divide both side by 4

x = 32/4

x = 8 ft

Thus,

Vr = 18x

x = 8 ft

Vr = 18 × 8

Vr = 144 ft³

Therefore, the volume of the rectangular prism is 144 ft³.

Vt = 14x

x = 8 ft

Vt = 14 × 8

Vt = 112 ft³

Therefore, the volume of the triangular prism is 112 ft³.

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