Question : The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 cm2, then find the length of each of the parallel sides (in cm).
Option 1: 27, 15
Option 2: 31, 19
Option 3: 29, 17
Option 4: 24, 12
Correct Answer: 29, 17
Solution :
Let the smaller parallel side be x cm.
So the longer parallel side can be written as (x + 12) cm.
The perpendicular distance between these two parallel sides is 60 cm.
The area of the trapezium = 1380 cm
2
⇒ $\frac{1}{2}$ × Sum of parallel sides × Height = 1380
⇒ $\frac{1}{2}$ × Sum of parallel sides × 60 = 1380
$\therefore$ Sum of parallel sides = 46
So, x + x + 12 = 46
⇒ 2x = 34
$\therefore$ x = 17 cm
Longer side = 17 + 12 = 29 cm
Hence, the correct answer is 29 cm, 17 cm.
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