Question

The area of a rectangle is `sqrt24` cm. lf its breadth is `(3-sqrt6)` cm, how do you find its length in the form `(a+bsqrt6)` cm where a and b are integers?

Answer 1

The length is `4+2sqrt6`

Explanation:

Area of rectangle (A) = length (L) * breadth(B). So length = area/breadth.

`L= A/B or L= sqrt24/(3-sqrt6) or L= (sqrt24*(3+sqrt6))/((3-sqrt6)*(3+sqrt6))`

or `L= (sqrt24*(3+sqrt6))/(9-6) = (3sqrt24+sqrt24*sqrt6)/3 =(3sqrt24+3sqrt16)/3 = (cancel3(2sqrt6+4))/cancel3= 4+2sqrt6`[Ans]