Question

The area of a trapezium is $475c{m}^2$and the height is $19cm$. Find the lengths of its two parallel sides if one side is $4cm$greater than the other.

Answer 1

Given

The area of a trapezium is $475c{m}^2$

The height of the trapezium is $19cm$

Length of parallel side is $4cm$ greater than the other

Let the given trapezium be $PQRS$, such that $PS\parallel RQ$ and $PQ$ be the height, as shown in the diagram

According to the given details

$PQ=height=19cm$

Let $RQ=xcm$ then $PS=(x+4)cm$

We know that ,

Area of trapezium$=\frac{1}{2}\times \left(sumofparallelsides\right)\times height$

So,

$$\begin{gathered} 475c{m}^2=\frac{1}{2}\left(PS+QR\right)\times PQ \\ \Rightarrow 475=\frac{1}{2}\left(x+4+x\right)\times 19 \\ \Rightarrow 475\times 2=\left(2x+4\right)\times 19 \\ \Rightarrow 950=\left(2x+4\right)\times 19 \\ \Rightarrow \frac{950}{9}=2x+4 \\ \Rightarrow 50-4=2x \\ \Rightarrow 46=2x \\ \Rightarrow x=\frac{46}{2}=23cm \end{gathered}$$

Thus,

$RQ=x=23cm$

and $PS=(x+4)=\left(23+4\right)cm=27cm$

Hence, its length of the two parallel sides are $23cm$and$27cm$