Question

Consider two congruent triangular prisms. Each rectangular face of prism A has a width of x + 2 and each rectangular face of prism B has a length of 2x + 1. If each rectangular face of prism A has an area of 5x + 10, what is the volume of prism B? (round to nearest whole number in cm3)

Answer 1

35
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Answer 2

`20√(3)`

Explanation:

Width of rectangular face of prism A = x+2

Area of rectangular face of prism A = 5x+10

So, length of rectangular face of prism A =
`(Area)/(Width) =(5x+10)/(x+2) =5`

Now , the length of rectangular face of prism B is 2x+1

Since we are given that the prisms are congruent

So, Length of rectangular face of both prisms must be equal

So,
`2x+1=5`

`2x=4`

`x=2`

So,the length of rectangular face of prism B = 2x+1 = (2*2)+1=5

Thus the height of prism = 5 cm

Volume of prism =
`\text{Area of equilateral triangle} * Height`

=
`(√(3))/(4) a^2 * Height`

Where a is the side of triangle

Side of triangle = width = x+2=2+2=4

So, Volume of prism =
`(√(3))/(4) a^2 * Height`

=
`(√(3))/(4) (4)^2 * 5`

=
`20√(3)`

Hence the volume of prism is
`20√(3)`