Question

the area of a trapezium is 180 sq. cm it's parallel sides are in the ratio 1:3 and the distance between them is 6cm. Find the length of each parallel sides​

Answer 1

Answer:

The length of each of the parallel sides are 15 cm and 45 cm.

Answer 2

Answer:

Given :-

• The area of a trapezium is 180 cm².
• It's parallel sides are in the ratio of 1 : 3 and the distance between them is 6 cm.

To Find :-

• What is the length of each parallel sides.

Solution :-

Let,

$\mapsto \bf First\: Parallel\: Sides_{(Trapezium)} =\: x\: cm$

$\mapsto \bf Second\: Parallel\: Sides_{(Trapezium)} =\: 3x\: cm$

Given :

• Parallel Sides = x and 3x
• Distance between them = 6 cm
• Area of Trapezium = 180 cm²

According to the question by using the formula we get,

$\footnotesize \implies \sf\boxed{\bold{Area_{(Trapezium)} =\: \dfrac{1}{2} \times (Sum\: of\: Parallel\: Sides) \times Distance\: between\: them}}$

$\implies \bf Area_{(Trapezium)} =\: \dfrac{1}{2} \times (a + b) \times h$

$\implies \sf 180 =\: \dfrac{1}{2} \times (x + 3x) \times 6$

$\implies \sf 180 \times \dfrac{2}{1} =\: 4x \times 6$

$\implies \sf \dfrac{360}{1} =\: 24x$

$\implies \sf 360 =\: 24x$

$\implies \sf \dfrac{360}{24} =\: x$

$\implies \sf 15 =\: x$

$\implies \sf\bold{x =\: 15}$

Hence, the required length of each parallel sides of a trapezium are :

$\dag$ First Parallel Sides Of Trapezium :

$\dashrightarrow \sf First\: Parallel\: Sides_{(Trapezium)} =\: x\: cm$

$\small \dashrightarrow \sf\bold{\underline{First\: Parallel\: Sides_{(Trapezium)} =\: 15\: cm}}$

$\dag$ Second Parallel Sides Of Trapezium :

$\dashrightarrow \sf Second\: Parallel\: Sides_{(Trapezium)} =\: 3x$

$\dashrightarrow \sf Second\: Parallel\: Sides_{(Trapezium)} =\: (3 \times 15)\: cm$

$\small \dashrightarrow \sf\bold{\underline{Second\: Parallel\: Sides_{(Trapezium)} =\: 45\: cm}}$

$\therefore$ The length of each parallel sides are 15 cm and 45 cm respectively.