Answer:
[tex]20\sqrt{3}[/tex]
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 = [tex]\frac{Area}{Width} =\frac{5x+10}{x+2} =5[/tex]
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, [tex]2x+1=5[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
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 = [tex]\text{Area of equilateral triangle} \times Height[/tex]
= [tex]\frac{\sqrt{3}}{4} a^2 \times Height[/tex]
Where a is the side of triangle
Side of triangle = width = x+2=2+2=4
So, Volume of prism = [tex]\frac{\sqrt{3}}{4} a^2 \times Height[/tex]
= [tex]\frac{\sqrt{3}}{4} (4)^2 \times 5[/tex]
=[tex]20\sqrt{3}[/tex]
Hence the volume of prism is [tex]20\sqrt{3}[/tex]
