A cuboid has a base area of 3 + \sqrt{5} cm^2 and a volume of 11 + 5\sqrt{5} cm^3. Find, without using a calculator, the height of the cuboid, in cm, in the form a + b\sqrt{5}, where a and b are integers.

\dfrac{11+5\sqrt{5}}{3-\sqrt{5}}

\dfrac{11-5\sqrt{5}}{3+\sqrt{5}}

AM-1381

Surds and rationalising

A Math · Secondary 4 · Medium · Surds and rationalising

A cuboid has a base area of

3 + \sqrt{5}

^2

and a volume of

11 + 5\sqrt{5}

^3

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

a + b\sqrt{5}

, where

a

and

b

are integers.

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