Question

Q11.

The diagram shows a trapezium.
x-4
Diagram NOT
accurately drawn
2x
x + 5
All the measurements are in centimetres.
The area of the trapezium is 351 cm2.
(a) Show that 2x2 + x - 351 = 0

Answer 1

Explanation:

The area of a trapezium is given as;

Area =
`(1)/(2)`(a + b)h

where: a is the length of the upper side, b is the length of its base and h is its height.

This implies that; a = x - 4, b = x + 5, h = 2x and area = 351

Thus,

351 =
`(1)/(2)`((x - 4) + (x + 50)) 2x

= (x - 4 + x + 5) x

531 = (2x + 1) x

= 2
`x^(2)` + x

So that;

2
`x^(2)` + x - 531 = 0

This gives a quadratic equation.