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 + 4. If each rectangular face of prism A has an area of 10x + 20, what is the volume of prism B? (round to nearest whole number in cm3)

Answer:The volume of prism B is 108 cm³Step-by-step explanation:* Lets study the information to solve the problem- Any triangular prism has five faces, two of them are triangles and the  other three are rectangles- Its two bases are triangles- Its side faces are rectangles- The volume of it is its base area × its height- The two triangular prisms are congruent, then all corresponding   dimensions are equal and their surface areas and volumes are equal * Now lets solve the problem∵ The two triangular prisms are congruent∴ All corresponding faces are congruent∵ The width of each rectangular faces in prism A = x + 2∴ The width of each rectangular faces in prism B = x + 2- The side of the triangular base is the width of the rectangular face∴ All sides of the triangular base in the prism B = x + 2∵ The area of the all rectangular face in prism A = 10x + 20∴ The area of the all rectangular face in prism B = 10x + 20∵ The length of each rectangular face in prism B is 2x + 2 - The length of the rectangular face of the triangular prism is its height∴ The height of the prism b = 2x + 4* Now lets find the value of x ∵ The rectangular face of prism B has width x + 2 , length 2x + 4    and area 10x + 20∵ The area of the rectangle = length × width∴ (2x + 4) × (x + 2) = 10x + 20 ⇒ simplify by using foil method∵ 2x(x) + 2x(2) + 4(x) + 4(2) = 10x + 20∴ 2x² + 4x + 4x + 8 = 10x + 20 ⇒ add the like term∴ 2x² + 8x + 8 = 10x + 20 ⇒ subtract 10 x from both sides∴ 2x² - 2x + 8 = 20 ⇒ subtract 20 from both sides∴ 2x² - 2x - 12 = 0 ⇒ divide all terms by 2 to simplify∴ x² - x - 6 = 0 ⇒ factorize it into two factors∵ x² = x × x∵ -6 = -3 × 2∵ -3x + 2x = -x∴ (x - 3)(x + 2) = 0- Equate each bracket by 0∴ x - 3 = 0 ⇒ add 3 to both sides ∴ x = 3OR∴ x + 2 = 0 ⇒ subtract 2 from both sides∴ x = -2 ⇒ we will refuse this value of x because there is no   negative dimensions∴ The value of x is 3 only- Lets find the dimensions of the prism B∵ Its width = x + 2∴ Its width = 3 + 2 = 5 cm∴ The sides of the triangular base are 5 cm∵ The triangular base is equilateral triangle∵ The area of any equilateral triangle = √3/4 (side)²∴ The area of the base = (√3/4) (5)² = 25√3/4 cm²∵ The height of the prism B = 2x + 4∵ x = 3∴ The height = 2(3) + 4 = 6 + 4 = 10 cm∵ The volume of any prism = its base area × its height ∴ The volume of prism B = 25√3/4 × 10 ≅ 108 cm³* The volume of prism B is 108 cm³