Question

the area of trapezium is 100cm² and its height is 8 cm find the length of the two parallel sides if one side is longer than the other by 5 cm​

Answer 1

Given:

Area of the trapezium = $100cm^{2}$

Height of the trapezium = $8cm$

Also given that, one side of the trapezium is longer than the other side by $5cm.$

To be found:

The length of the two parallel sides of the trapezium.

Note:

• Trapezium: Trapezium is a closed figure with four sides, in which, two sides are parallel to each other and the other two sides are non-parallel.
• An image is attached with the solution,  for reference.

Formula to be used:

In this problem, the required formula is the formula for the area of trapezium.

Let the area of trapezium be denoted by "$A$".

Let the height of the trapezium be denoted by "$h$".

Let the two parallel sides be denoted by "$a$" and "$b$".

Now, the area of the trapezium is given by:

$A=(1/2)h(a+b)$.........(1)

Solution:

As per the given data, one of the two parallel sides is longer than the other by $5cm.$

⇒$b=a+5$........(2)

Now,

$A=(1/2)h(a+b)\\100=(1/2)*8*(a+a+5)\\100=(1/2)*8*(2a+5)\\100=4(2a+5)\\2a+5=(100/4)\\2a+5=25\\2a=25-5\\2a=20\\a=10cm$

From the value of "$a$", the value of "$b$" can be found using the equation (2), which is given by:

$b=a+5\\b=10+5\\b=15cm$

Final Answer:

The required lengths of two parallel sides are $15cm$ and $10cm$.