Answer:
[tex]18\text{cm}[/tex]
Step-by-step explanation:
[tex]\text{Solution: }\\\text{Length of base of right triangle}(b)=12\text{cm}\\\text{Length of hypotenuse}(h)=13\text{cm}\\\text{Length of remaining side }(p)=?\\\\\text{Using pythagoras theorem,}\\\\p=\sqrt{h^2-b^2}=\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\text{cm}\\\\\therefore\ \text{AB = DE = 5cm}[/tex]
[tex]\text{Let the length of the prism be }l.\\\text{According to the question,}[/tex]
[tex]\text{Total Surface Area = 660cm}^2\\\text{or, Area of }(\triangle\text{ABC}+\triangle\text{FED + rect.ABDE + rect.BCFE + rect.ACFD})=660\\\\\text{or, }\dfrac{1}{2}\times12\times5+\dfrac{1}{2}\times12\times5+5l+12l+13l=660\\\\\text{or, }60+60+30l=660\\\text{or, }30l=540\\\text{or, }l=18\text{cm}[/tex]
