Question

The difference between the two parallel sides of a trapezium is 8 cm.perpendicular distance between them is 38 cm.lf the area of the trapezium is 950 cm,find the lengths of the parallel sides

Answer 1

Answer:

29 cm and 21 cm

Step-by-step explanation:

Given - area of trapezium is 950, height ( perpendicular distance) is 38 cm

Area = 1/2*(a+b) * h. ( a and b are the

parallel sides ,

and h is height)

So, 950 =1/2 * ( a+ b) * 38

950 = ( a+ b) * 19

950/19 = ( a + b)

50 = ( a+b)

In the question, it also states that a - b = 8

So the lengths of the parallel sides can be 29 cm and 21 cm as 29 + 21 = 50 cm and 29 - 21 = 8 cm

Therefore the answer is 29 cm and 21 cm

Answer 2

Given :

• The difference between the parallel sides of the trapezium is 8 cm.
• The perpendicular distance (height) between is 38 cm.
• Area of the trapezium is 950 cm²

To Find :

• Length of parallel sides of the trapezium.

Solution :

Let the first parallel side be x cm.

Let the other parallel side be y cm.

Case 1 :

The difference between the first parallel, x and the second parallel side, y is 8 cm.

Equation :

$\sf{\longrightarrow{x-y=8}}$

$\sf{\longrightarrow{x=8+y\:\:\:(1)}}$

Case 2 :

The area of the trapezium is 950 cm².

Height of the trapezium = 38 cm.

Formula :

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

Equation :

$\sf{\longrightarrow{950\:=\:\dfrac{1}{2}\:\times\:(x+y)\:\times\:38}}$

$\sf{\longrightarrow{950\:=\:\dfrac{1}{2}\:\times\:(38x+38y)}}$

$\sf{\longrightarrow{950\:\times\:2=\:38x+38y}}$

$\sf{\longrightarrow{1900=38x+38y}}$

$\sf{\longrightarrow{1900=38(x+y)}}$

$\sf{\longrightarrow{\dfrac{1900}{38}=x+y}}$

$\sf{\longrightarrow{50=x+y}}$

$\sf{\longrightarrow{50=8+y+y}}$

$\bold{\big[From\:equation\:(1)\:x\:=\:8+y\:\big]}$

$\sf{\longrightarrow{50-8=y+y}}$

$\sf{\longrightarrow{42=2y}}$

$\sf{\longrightarrow{\dfrac{42}{2}=y}}$

$\sf{\longrightarrow{21=y}}$

Substitute, y = 21 in equation (1),

$\sf{\longrightarrow{x=8+y}}$

$\sf{\longrightarrow{x=8+21}}$

$\sf{\longrightarrow{x=29}}$

$\large{\boxed{\bold{\red{First\:parallel \:side\:=\:x\:=\:29\:cm}}}}$

$\large{\boxed{\bold{\red{Second\:parallel \:side\:=\:y\:=\:21\:cm}}}}$