The diagram in Figure $1$ shows a sign in the shape of a rectangle $ABCD$ with a semicircle join

Question

The diagram in Figure $1$ shows a sign in the shape of a rectangle $ABCD$ with a semicircle joined to $CD$. The length of $AB$ is $2x$ cm. The total perimeter of the sign is $50$ cm. Show that the area of the sign in Figure $1$ is $50x - 2x^2 - \frac{\pi x^2}{2}$.[2] An equilateral triangle with the side of $0.25x$ cm is to be removed from the sign as shown in Figure $2$. The area of the new sign is to be as large as possible. Use differentiation to find the value of $x$ that will give the maximum area of the new sign.[5]

Accepted Answer

(ii) x=6.95

2024 ASRJC H1 Q2

2024 ASRJC H1 Q2