A rectangular piece of paper $ABCD$ is folded along the line $EC$ such that $D$ is moved

Question

A rectangular piece of paper $ABCD$ is folded along the line $EC$ such that $D$ is moved to $F$. The length of $AB$ is $\left( 3x+1 \right)$ cm, $BC$ is $\left( 2x-3 \right)$ cm and $ED$ is $3$ cm. Write down, in terms of $x$, an expression for the area of rectangle $ABCD$. Write down, in terms of $x$, an expression for the area of the triangle $CDE$. Given that the area of the shaded region $ABCFE$ is $64$ cm$^{2}$, form an equation in $x$ and show that it reduces to $3{{x}^{2}}-8x-35=0$. By solving the equation $3{{x}^{2}}-8x-35=0$, find the length $AB$.

Accepted Answer

(a) $6x^2 - 7x - 3$ (b) $\frac{9}{2}x + \frac{3}{2}$ (c) Shown (d) $AB = 16$ cm

Area and Folding Problem Involving a Quadratic Equation

Area and Folding Problem Involving a Quadratic Equation

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