Question

The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism. Find the volume of each figure. Rectangular prism: L= 6 ft. W= x H=3 ft. Triangular Prism: L= 7 ft W= x H=4 ft. Volume of rectangular prism: _ ft3 Volume of triangular prism: _ ft3 PLEASE ANSWER ASAP! I'M OFFERING A LOT OF POINTS!

Answer 1

Answer:

Step-by-step explanation:

Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT

Since VR = length * width and height

VR = 6*x*3

VR = 18x ft³

Also VT =  Length *width * Height/2

VT = (7 * x * 4)/2

VT = 28x/2

VT = 14xft³

Since VR = 32 + VT

18x = 32+(14x)

collect like terms

18x-14x = 32

4x = 32

divide both sides by 4

4x/4 = 32/4

x = 8

Volume of the rectangular prism = 18x

Volume of the rectangular prism = 18*8

Volume of the rectangular prism = 144ft³

Volume of the right triangular prism = 14x

Volume of the rectangular prism = 14*8

Volume of the rectangular prism = 112ft³

Answer 2

Answer:

rectangular is 114ft and triangular is 112ft

Step-by-step explanation:

Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT

Since VR = length * width and height

VR = 6*x*3

VR = 18x ft³

Also VT =  Length *width * Height/2

VT = (7 * x * 4)/2

VT = 28x/2

VT = 14xft³

Since VR = 32 + VT

18x = 32+(14x)

collect like terms

18x-14x = 32

4x = 32

divide both sides by 4

4x/4 = 32/4

x = 8

Volume of the rectangular prism = 18x

Volume of the rectangular prism = 18*8

Volume of the rectangular prism = 144ft³

Volume of the right triangular prism = 14x

Volume of the rectangular prism = 14*8

Volume of the rectangular prism = 112ft³