# Base of a right prism is a triangle having ratio of sides 3:4:5. Height of the prism is 12 cm and total surface area of the prism is 576 cm2. What is its volume?

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by rajanc

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by rajanc

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lets say the three sides are 3x , 4x, 5x

s = (3x + 4x + 5x) / 2 = 6x

Area = sqrt(6x (6x-3x)(6x-4x)(6x-5x) )

Area = sqrt(6x (3x)(2x)(1x))

Area = sqrt(36x)

Area = 6x sq. units.

Height of the prism is 12cm

so the surface area {(2*6x)+(3x+4x+5x)*12}

=12x+144x=156x

156x=576 cm2

=> x=3

and the formula of volum is= triangle area x prism height

i think you can do the rest....