Question
The difference between two parallel sides of a trapezium is 8 cm . The perpendicular distance between them is 19 cm . While the area of trapezium is $760 cm^2$. What will be the length of the parallel sides?
✓
Answer
Let the two parallel sides be $a$ and $b$. According to the question,
$
a-b=8
$
Area of trapezium
$
\begin{array}{cc}
& =\frac{1}{2} \times h(a+b) \\
\Rightarrow & \frac{1}{2}(a+b) \times 19=760 \\
\Rightarrow & a+b=40 \times 2 \\
\Rightarrow & a+b=80
\end{array}
$
From Eqs. (i) and (ii), we get
$
\begin{aligned}
2 a & =88 \\
\Rightarrow \quad a=\frac{88}{2} & =44
\end{aligned}
$
From Eq. (i), we get
$
\begin{aligned}
& a-b=8 \\
\Rightarrow & b=a-8=44-8=36 cm \\
\therefore & a=44 cm \text { and } b=36 cm
\end{aligned}
$
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