A rectangular box has length 3+\sqrt{5} m and breadth \sqrt{5}-1 m. Its volume is 18\sqrt{5}-30 m^3. Find the height of the box in the form a+b\sqrt{5} m, where a and b are integers.

AM-281

Surds and rationalising

A Math · Secondary 3 · Hard · Surds and rationalising

A rectangular box has length

3+\sqrt{5}

m and breadth

\sqrt{5}-1

m. Its volume is

18\sqrt{5}-30

^3

. Find the height of the box in the form

a+b\sqrt{5}

m, where

a

and

b

are integers.

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