The diagram shows a shape made by cutting an equilateral triangle out of a rectangle of width $x$

Question

The diagram shows a shape made by cutting an equilateral triangle out of a rectangle of width $x$ cm. The perimeter of the shape is $20$ cm. Show that the area, $A$ $\text{cm}^2$, of the shape is given by $A = 10x - \left(\frac{6 + \sqrt{3}}{4}\right)x^2$.[3] Given that $x$ can vary, find the value of $x$ which produces the maximum area and calculate this maximum area. Give your answers to $2$ significant figures.[4]

Accepted Answer

(ii) $x = 2.6$ ($2$ s.f.), $A = 13$ ($2$ s.f.)

2024 FMSS PRELIMS P1 Q5

2024 FMSS PRELIMS P1 Q5