The diagram shows a trapezium.

Show that x^2+20x=400

The lengths of the parallel sides of the trapezium are x cm and 20cm. The height of the trapezium is 2x cm. The area is 400cm^2.

Expert Answers

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You need to remember the area of trapezium such that:

Area trapezium = Area of rectangle + Area of triangle

You need to consider the dimensions of rectangle such that: one of parallel sides of trapezium x is length of rectangle and height of trapezium 2x represents the width of rectangle.

You need to consider the dimensions of triangle such that: the base of triangle is `(20 - x)`  and the height is `2x` .

Area trapezium = `x*2x + (1/2)*(20 - x)*2x`

Factoring out 2x and substituting 400 for area of trapezium yields:

`400 = 2x(x + 10 - x/2) =gt 400 = x + 20x^2`

Hence, the last line proves the identity `400 = x + 20x^2`  under the given conditions.

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