Base of prism

The base of the perpendicular prism is a rectangular triangle whose legs lengths are at a 3:4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.

Correct answer:

V =  540 cm3

Step-by-step explanation:

S=468 cm2 a:b = 3:4 h = b2  a2 + b2 = c2 a = 3x b = 4x c = 5x 32+42 = 52  S = ab + (a+b+c)h S = 3 4 x2 + (3x+4x+5x)(4x2)  3 4 x2+(3x+4x+5x)(4x2)=468  3 4 x2+(3x+4x+5x)(4x2)=468 60x224x468=0 60=2235 24=233 468=223213 GCD(60,24,468)=223=12  5x22x39=0  a=5;b=2;c=39 D=b24ac=2245(39)=784 D>0  x1,2=2ab±D=102±784 x1,2=102±28 x1,2=0.2±2.8 x1=3 x2=2.6  x>0 x=x1=3 cm  a=3 x=3 3=9 cm b=4 x=4 3=12 cm c=5 x=5 3=15 cm h=b2=122=10 cm  S2=a b+(a+b+c) h=9 12+(9+12+15) 10=468 cm2 S2=S  V=2a b h=29 12 10=540 cm3

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