Science:Math Exam Resources/Courses/MATH102/December 2019/Question 12/Statement

A 90cm piece of wire is used to create an equilateral triangle, and a rectangle that is twice as long as it is wide. Determine whether and where to cut the wire such that the sum of the areas of the two shapes is maximized.

Note: the area of an equilateral triangle with side length $\ell$ is ${\frac {\sqrt {3}}{4}}\ell ^{2}$. As always, completely justify your answer.