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Question

Area of a trapezium is $$160\ sq.cm$$. Lengths of parallel sides are in the ratio $$1:3$$. If smaller of the parallel sides is $$10\ cm$$ in length, then find the perpendicular distance between them.


Solution

Given,
Area of trapezium $$=160\ m^2$$
The ratio of the length of its parallel sides $$=1:3$$
Smaller parallel sides $$=10\ cm$$

$$\therefore$$  Length of greater side $$=10\times 3=30\ cm$$

Let the distance between them $$=h$$

We know that, 
Area $$=\dfrac12\times$$ sum of parallel sides $$\times$$ height 
$$\Rightarrow 160=\dfrac12(30+10)h\\ \Rightarrow 160\times 2=40h\\ \Rightarrow h=\dfrac{320}{40}=8\ cm$$

Mathematics

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