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The base of a right prism is a rightd-angle triangle. The height and volume of prism is 8 cm and 240 cm3 respectively. If one perpendicular side of base is 7 cm more than the other perpendicular side, then what is the total surface area of the prism?

The base of a right prism is a rightd-angle triangle. The height and volume of prism is 8 cm and 240 cm3 respectively. If one perpendicular side of base is 7 cm more than the other perpendicular side, then what is the total surface area of the prism? Correct Answer 300 cm<sup>2</sup>

Let the two perpendicular sides of the base of prism is ‘x’ and ‘x + 7’ respectively.

Base area of prism = (1/2) × x × (x + 7) = Volume of prism/Height of prism

x(x + 7) = 2 × (240/8)

x(x + 7) = 60

x = 5 and -12 (Not valid)

Two perpendicular sides of base are 5 cm and 12 cm respectively.

Third side of the base = √(52 + 122) = 13 cm

Lateral surface area of the prism = Perimeter of base × Height = (5 + 12 + 13) × 8 = 240 cm3

Total surface area of the prism = 240 + (2 × Base area of prism)

= 240 + (2 × 30) = 300 cm2

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