Question

X + 2

Answer 1

Answer:

see explanation

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = $\frac{1}{2}$ 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 = $\frac{1}{2}$(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