Question

the area of a trapezium is 180cm² and its height is 12cm. if one of the parallel sides is double that of the other, find
The two parallel sides.


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Answer 1

Given :

• Area of trapezium is 180 cm²
• Height of the trapezium is 12 cm.
• One parallel side is double that of the other one.

To Find :

• Two parallel sides.

Solution :

Let the first parallel side be x cm.

Let the second parallel side be y cm.

Case 1 :

One side is double of the other side.

Equation :

$\sf{\longrightarrow{x=2y}}$

$\sf{\dfrac{x}{2}=y\:\:\:(1)}$

Case 2 :

Area of trapezium is 180 cm² and height is 12 cm.

Formula :

$\large{\boxed{\bold{Area_{Trapezium}\:=\:\dfrac{1}{2}\:\times\:(sum\:of\:parallel\:sides)\:\times\:height}}}$

Equation :

$\sf{\longrightarrow{180\:=\:\dfrac{1}{2}\:\times\:(x+y)\:\times\:12}}$

$\sf{\longrightarrow{180\:=\:\dfrac{1}{2}\:\times\:(12x+12y)}}$

$\sf{\longrightarrow{360\:=12x+12y}}$

$\sf{\longrightarrow{360=12(x+y)}}$

$\sf{\longrightarrow{\dfrac{360}{12}=x+y}}$

$\sf{\longrightarrow{30=x+y}}$

$\sf{\longrightarrow{30\:=\:x+\dfrac{x}{2}}}$

$\sf{\longrightarrow{30=\dfrac{2x+x}{2}}}$

$\sf{\longrightarrow{30=\dfrac{3x}{2}}}$

$\sf{\longrightarrow{30\:\times\:2=3x}}$

$\sf{\longrightarrow{60=3x}}$

$\sf{\longrightarrow{\dfrac{60}{3}=x}}$

$\sf{\longrightarrow{20=x}}$

Substitute, x = 20 in equation (1)

$\sf{\longrightarrow{\dfrac{x}{2}=y}}$

$\sf{\longrightarrow{\dfrac{20}{2}=y}}$

$\sf{\longrightarrow{10=y}}$

$\large{\boxed{\bold{First\:parallel\:side\:=\:x\:=\:20\:cm}}}$

$\large{\boxed{\bold{Second\:parallel\:side\:=\:y\:=\:10\:cm}}}$

Answer 2

GIVEN:

Area of trapezium = 180cm²

Height of the trapezium = 12cm

One of the parallel sides is double the others.

TO FIND:

The two parallel sides of trapezium

SOLUTION:

Let the parallel sides of trapezium be x and 2x

We know that,

Area of trapezium = 1/2 [ sum of parallel sides] × h

180 = 1/2 [ x + 2x ] × 12

==> 180 = 3x × 6

==> 180 = 18x

==> x = 180/18

==> x = 10cm

One of the side = x = 10cm

Another side = 2x = 2 × 10 = 20cm

Therefore, the sides are 10cm and 20cm.