Question
If 3a = 4b = 6c and a + b + c = `27sqrt(29)`, then `sqrt(a^2 + b^2 + c^2 )` is :
Answer: Option C
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`:.` `sqrt(a^2 + b^2 + c^2)` = `sqrt((a + b + c)^2 - 2(ab + bc + ca))`
= `sqrt((27sqrt(29))^2 - 2(2c xx 3/2 c + 4/2 c xx c + c xx 2c))`
=`sqrt((729xx 29) - 2(3c^2 + 3/2 c^2 + 2c^2))`
= `sqrt((729 xx 29) - 2 xx 13/2 c^2)`
=`sqrt((729 xx 29) - 13 xx (6sqrt(29))^2)`
= `sqrt(29(729 - 468))`
=`sqrt(29 xx 261)` = `sqrt(29 xx 29 xx 9)` = 29 x 3 = 87.
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