Question

The lengths of the parallel sides of a trapezium are ( x + 9 ) cm and ( 2x -3 ) cm and the distance between them is ( x + 4 ) cm. If its area is 540 cm^2, find x.

Answer 1

Answer:

x = 16

Step-by-step explanation:

area of trapezium = 1/2 h ( a + b)

h = height = x + 4

a and b are the parallel side of trapezium

a = x + 9

b = 2x - 3

area= 540 sq cm

$540 = \frac{1}{2} (x + 4)(x + 9 + 2x - 3) \\ 540 = \frac{1}{2} (x + 4)(3x + 6) \\ 540 = \frac{1}{2} (3 {x}^{2} + 6x + 12x + 24) \\ 540 = \frac{1}{2} (3 {x}^{2} + 18x + 24) \\ 540 \times 2 = 3( {x}^{2} + 6x + 8) \\ \frac{540 \times 2}{3} = {x}^{2} + 6x + 8 \\ 180 \times 2 = {x}^{2} + 6x + 8 \\ 360 = {x}^{2} + 6x + 8 \\ {x}^{2} + 6x + 8 - 360 = 0 \\ {x}^{2} + 6x - 352 = 0 \\ {x}^{2} + 22x - 16x - 352 = 0 \\ x(x + 22) - 16(x + 22) = 0 \\ (x + 22)(x - 16) = 0 \\ x + 22 = 0 \: \: \: \: \: x - 16 = 0 \\ x = - 22 \: \: \: \: \: \: \: \: \: \: \: x = 16$

as the length of line cannot be negative we take the positive value of x = 16

a = x + 9 = 16 + 9 = 25 cm

b = 2x - 3 = 2(16) - 3 = 32 - 3 = 29 cm

h = x + 4 = 16 + 4 = 20 cm

hope you get your answer