Question

The area of a trapezium is \[720c{{m}^{2}}\] the ratio of the parallel sides is \[2:1\] if the distance between the parallel sides is \[20cm\] find the length of the parallel sides.
A) \[20,30cm\]
B) \[24,48cm\]
C) \[42,46cm\]
D) none of these

Answer 1

Hint: From the given question we have been given that area of a trapezium and ratio of the parallel sides and we are asked to find the length of parallel sides. We will use the area of trapezium formula which is \[\dfrac{1}{2}h\left( a+b \right)\] and solve the equation with the help of basic mathematical operations like multiplications etc.

Complete step-by-step answer:
From the given question we have given the sides ratio as \[2:1\].
So, let us assume that the length of those parallel sides as \[2x,x\]
We know that from the geometry the area of trapezium will be as follows.
\[\Rightarrow area=\dfrac{1}{2}h\left( a+b \right)\]
Where the parameters \[a,b\] are lengths of parallel sides,
So, now we will use the substitution method and substitute the given values in the above formulae. So, we get the solution as follows.
\[\Rightarrow \dfrac{1}{2}h\left( a+b \right)=720\]
\[\Rightarrow \dfrac{1}{2}20\left( 2x+x \right)=720\]
\[\Rightarrow 10\left( 3x \right)=720\]
\[\Rightarrow x=24\]
We got the length of the side as \[\Rightarrow x=24\]. So, the other side will be as follows.
\[\Rightarrow 2x=2\times 24=48\]
Therefore, the lengths of the sides will be \[24,48\]
The figure will be as follows.

Note: Students should do the calculations very carefully. Students should have good knowledge in the concept geometry mainly trapezium and its formulae. We should know the formulae of area of trapezium which is
\[\Rightarrow area=\dfrac{1}{2}h\left( a+b \right)\] to solve the question.