A cuboid has base area 5 + 2\sqrt{3} cm^2 and volume 14 + 8\sqrt{3} cm^3. Find, without using a calculator, the height of the cuboid in the form a + b\sqrt{3}, where a and b are integers.

\dfrac{22}{13} + \dfrac{12}{13}\sqrt{3}

\dfrac{22}{13} - \dfrac{12}{13}\sqrt{3}

\dfrac{14}{5} + \dfrac{8}{5}\sqrt{3}

AM-1377

Surds and rationalising

A Math · Secondary 4 · Hard · Surds and rationalising

A cuboid has base area

5 + 2\sqrt{3}

^2

and volume

14 + 8\sqrt{3}

^3

. Find, without using a calculator, the height of the cuboid in the form

a + b\sqrt{3}

, where

a

and

b

are integers.

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