Question

The area of a trapezium is $$182cm^2$$. Its height is $$14cm$$. The larger parallel side is longer than the other by $$16cm$$. Find the length of the parallel sides.

Solution

Given Area of Trapezium$$=182cm^2,h=14cm$$Let the upper parallel side be $$x$$other side $$=x+16$$ cmArea of Trapezium $$=\dfrac{1}{2}h\left(a+b\right)$$ where $$a$$ and $$b$$ are the parallel sides$$\therefore 182=\dfrac{1}{2}\times 14\left(x+x+16\right)$$$$\Rightarrow 182=7\left(2x+16\right)$$$$\Rightarrow 182=14\left(x+8\right)$$$$\Rightarrow \left(x+8\right)=\dfrac{182}{14}=13$$$$\Rightarrow x=13-8=5$$$$\therefore$$ the shorter parallel side$$=5$$cm and the base of the Trapezium $$=5+16=21$$cmMathematics

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