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)

see explanation

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = 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 = (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

yes

step-by-step explanation: