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x + 2
Diagram NOT
accurately drawn
x-5
x + 6
The diagram shows a trapezium.
The lengths of three of the sides of the trapezium are x - 5, x + 2 and x + 6.
All measurements are given in centimetres.
The area of the trapezium is 36 cm.
(a) Show that x^2- x - 56 = 0

-look at the picture (a)

x 2 Diagram NOT accurately drawn x5 x 6 The diagram shows a trapezium The lengths of three of the sides of the trapezium are x 5 x 2 and x 6 All measurements ar class=

Respuesta :

Answer:

see explanation

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (a + b)

where a, b are the measures of the parallel sides and h the perpendicular distance between them.

here h = x - 5, a = x + 6 and b = x + 2, thus

A = [tex]\frac{1}{2}[/tex](x - 5)(x + 6 + x + 2) = 36

Multiply both sides by 2 to clear the fraction

(x - 5)(2x + 8) = 72 ← expand left side

2x² - 2x - 40 = 72 ← divide through by 2

x² - x - 20 = 36 ( subtract 36 from both sides )

x² - x - 56 = 0 ← as required