Question

The ratio of parallel sides of trapezium is 4: 5 and the distance between them is 12 cm . If the area of the trapezium is 189cmsq find the length of parallel sides

Answer 1

Define x:

Ratio of the parallel sides = 4 : 5

Let x be the constant ratio

Ratio of the parallel sides = 4x : 5x

Solve x:

Area = 1/2 (a + b ) x h where a and b are the length of the parallel sides and h, height

Given area = 189 cm²  and h = 12 cm

189 = 1/2 (4x + 5x) 12

189 = 6(9x)

189 = 54x

x = 3.5 cm

Find the length of the parallel sides:

4x = 4(3.5) = 14 cm

5x = 5(3.5) = 17.5 cm

Answer: The two parallel sides are 14 cm and 17.5 cm

Answer 2

let the lengths are 4x,5x
(a+b)/2=area of trapezius
(4x+5x)/2=189
9x=378
x =42

4x=168,5x=210
lengths are (168,210)
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