The diagram shows a triangular plot of ground, $ABC$, in which $AB=6$ m, $AC=a$ m and angle \(

Question

The diagram shows a triangular plot of ground, $ABC$, in which $AB=6$ m, $AC=a$ m and angle $BAC$ is a right angle. A gardener considers using a rectangular part, $APQR$, of the triangle, where $P$, $Q$ and $R$ lie on $AB$, $BC$ and $AC$ respectively, to grow vegetables. Given that $AR=x$ m, show that $AP=6-\frac{6}{a}x$ m.[2] Given that $x$ can vary, find the largest possible area of the vegetable plot $APQR$, giving your answer in terms of $a$. Justify that this is a maximum value.[4] Given instead that the vegetable plot $APQR$ is a square, find $x$ in terms of $a$.[1]

Accepted Answer

(b)$x=\frac{1}{2}\alpha, $maximum area = $\frac{3}{2}\alpha$ m$^2$ (c)$x=\frac{6\alpha}{\alpha+6}$

2024 YIJC H1 Q3

2024 YIJC H1 Q3