Mathematics

Problem

In a right-angled triangle

XYZ

with

\angle Z = 90^\circ

, the perimeter of the triangle is

30\,\text{cm}

and the acute angle

\angle X = 60^\circ

. (i) Express the lengths of

YZ

(opposite

\angle X

) and

XZ

(adjacent to

\angle X

) in terms of a single variable. (ii) Form an equation in that variable using the perimeter and solve for the exact lengths of all three sides. (iii) Calculate the area of

\triangle XYZ

in square centimetres.

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