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

Answer:

$20\sqrt{3}$

Step-by-step 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 = $\frac{Area}{Width} =\frac{5x+10}{x+2} =5$

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 = $\text{Area of equilateral triangle} \times Height$

                            = $\frac{\sqrt{3}}{4} a^2 \times Height$

Where a is the side of triangle

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

So, Volume of prism = $\frac{\sqrt{3}}{4} a^2 \times Height$

                                   = $\frac{\sqrt{3}}{4} (4)^2 \times 5$

                                   =$20\sqrt{3}$

Hence the volume of prism is    $20\sqrt{3}$