Edexcel IGCSE Math A 2.7.HC form quadratic equations from context

Practise the context-quadratic question by translating trapezium dimensions and area into algebra, then simplifying to the requested equation.

Exam points

Form an area equation from labelled dimensions before expanding and simplifying.
Show the algebraic steps that prove the requested quadratic equation exactly.

[Maximum number: 3]

The diagram shows a trapezium.

Diagram NOT accurately drawn

All measurements shown on the diagram are in centimetres.
The area of the trapezium is $133 \mathrm{~cm}^{2}$

Show that $8 x^{2}-6 x-275=0$

Area of the trapezium:
$\frac12\bigl(x+5+3x-2\bigr)(2x-3)=133$ $\frac12(4x+3)(2x-3)=133$ $8x^2-12x+6x-9=266$ $8x^2-6x-275=0$

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