Question

In a trapezium shaped field, one of the parallel sides is twice the other. If the area of the field is 9450${m^2}$ and perpendicular distance between the two parallel sides of 84$cm$ . find the length of the longer of the parallel sides.

Answer 1

Hint:
 Compare the given area with the formula of area of trapezium to get the required answer.
Since the area of trapezium is given, Equate the area of trapezium to the given area.

Complete step-by-step answer:
Given: we have given the area of trapezium which is 9450${m^2}$ and height of trapezium is 84$m$ and one side is twice the other parallel side.
First, we will let smaller side of the trapezium be $x$
Which means the longer side will be $2x$ because this side is double the smaller side.
And we know that the area of trapezium is given by half of the product of height and sum of two parallel sides.
Area $ = \dfrac{1}{2}\left( {a + b} \right)h$
Where, $a$ is the smaller side and $b$ is the longer side and $h$ is the height of trapezium given
Now, substitute the values of area and height given to us and parallel sides which were let by us.
$
  \dfrac{1}{2} \times \left( {x + 2x} \right) \times 84 = 9450 \\
  126x = 9450 \\
  x = \dfrac{{9450}}{{126}} \\
  x = 75m \\
$
So, the length of smaller side of trapezium shaped field is $75m$
And length of the longer side was $2x$
Substitute the value of $x$ in $2x$ to find the longer length as the longer side is double of the smaller side.
Mathematically, $2 \times 75 = 150m$
So, the length of the longer parallel side is $150m$.

Note:
The dimension for all terms should be in metre form and use the formula of area of trapezium and then find the lengths of the trapezium shaped field which are parallel.