Question

the area of trapezium is 180 cm^2 and its height is 15 cm.if one of the parallel side is double of other, find the length of two parallel sides

Answer 1

GiveN :-

• Area of Trapezium is 180 cm²

• Height of Trapezium is 15 cm

• One parallel side of trapezium is double of other

To FinD :-

• Length of two Parallel Sides

SolutioN :-

Let one Parallel side be x

As Given that One parallel side of trapezium is double of other . So ,

Other Parallel side = 2x

$\longmapsto\boxed{ \bf Area=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}\\ \\ \longmapsto\tt{180=\dfrac{1}{2}\times{(x+2x)}\times{15}}\\ \\ \longmapsto\tt{180\times{2}=(x+2x)\times{15}}\\ \\ \longmapsto\tt{360=15x+30x}\\\\ \longmapsto\tt{360=45x} \\ \\ \longmapsto\tt{x=\cancel\dfrac{360}{45}} \\ \\ \longmapsto\boxed{\bf{x=8}}$

Therefore :-

• One Parallel side = x = 8 cm

• Other Parallel side = 2x = 16 cm

So , The Length of Two parallel sides are 8 cm and 16 cm

Answer 2

Given :

• Area of Trapezium = 180 cm²
• Height of Trapezium = 15 cm
• One parallel side of trapezium is double of other

To Find :

• Length of two Parallel Sides

Solution :

Let one parallel side = x cm

We are given that One parallel side of trapezium is double of other. Therefore,

Other parallel side = 2x cm

We know that,

$\boxed{\bf Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

By Putting Values :

$\implies \bf{180=\dfrac{1}{2}\times{(x+2x)}\times{15}}$

$\implies \bf{180\times{2}=(x+2x)\times{15}}$

$\implies \bf{360=15x+30x}$

$\implies \bf{360=45x}$

$\implies \bf{x=\dfrac{360}{45}}$

$\implies \bf{x=8}$

Value of x is 8.

Therefore

• One parallel side = x cm = 8 cm
• Other parallel side = 2x = 2 × 8 cm = 16 cm

Hence, The Length of Two parallel sides are 8 cm and 16 cm.