Answer:
The volume of the rectangular prism is 144 ft³.
The volume of the triangular prism is 112 ft³.
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.