the lengths of three unequal egdes of a rectangular solids block are i – InterviewSolution

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1.	the lengths of three unequal egdes of a rectangular solids block are in GP .if the volume of the block is 26 `cm^(3)` and the total surface area is `252cm ^(2)` then the length of the longest edge is
Answer» Let the lengths of its edges be `a/r` cm, a cm and ar cm. Then, its volume `=(a/rxxaxxar) cm^(3)=a^(3) cm^(3)`. `:. a^(3)=216=6^(3) rArr a=6`. So, the edges are 6r cm, 6 cm and `6/r` cm. `:.` surface area `=2[lb+bh+lh]` `=2[6rxx6+6xx6/r+6rxx6/r] cm^(2)` `=2[36r+36/r+36] cm^(2) =72 xx[r+1/r+1] cm^(2)`. `:. 72 xx(r+1/r+1)=252` `rArr 2(r^(2)+1+r)=7r rArr 2r^(2)-5r+2 =0` `rArr (r-2) (2r-1) =0 rArr r=2` or `r=1/2`. Each value of r gives the longest edge `=12` cm.

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