Optional extension Square $ABCD$ has side $9$ cm. Points $E,F$ satisfy $AE=BF=x$ cm. The sha

Question

Optional extension Square $ABCD$ has side $9$ cm. Points $E,F$ satisfy $AE=BF=x$ cm. The shaded region is the square excluding triangle $EBF$. Express its area $S$ in terms of $x$. If $S=72\text{ cm}^2$, show that $x^2-9x+18=0$. Solve it. If $CF>BF$, express the area of triangle $ECF$ as a percentage of the square. $A$ $B$ $C$ $D$ $E$ $F$ $9\text{ cm}$ $x\text{ cm}$ $x\text{ cm}$

Accepted Answer

(a) $S=81-\dfrac12x(9-x)$ (c) $x=3,6$ (d) $\dfrac{200}{9}\%$ (using $x=3$). (b) $x^2-9x+18=0$ (shown).

Shaded square-minus-triangle area

Shaded square-minus-triangle area

Solution:

Solution locked