$ABCD$ is a rectangle when $AB=\left( 3x+5 \right)$ cm and $BC=\left( 2x+8 \right)$ cm. \

Question

$ABCD$ is a rectangle when $AB=\left( 3x+5 \right)$ cm and $BC=\left( 2x+8 \right)$ cm. $XYZ$ is a right-angled triangle in which $XY=\left( 6x \right)$ cm and $XZ=\left( 5x-1 \right)$ cm. The area of the rectangle $ABCD$ is equal to the area of the triangle $XYZ$. Form an equation, in terms of $x$, and show that it reduces to $9{{x}^{2}}-37x-40=0$. By solving the equation in (a), find the length of $BC$. Explain why one of the solutions in (b) is rejected.

Accepted Answer

(a) $9x^2-37x-40=0$ (b) $BC=18\text{ cm}$ (c) Reject $x=-\frac{8}{9}$ because lengths must be positive.

Quadratic Equation from Area of Rectangle and Triangle

Quadratic Equation from Area of Rectangle and Triangle

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