Question

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

Answer 1

QUESTION:-

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

Given:-

Area of the trapezium = 100cm²

Height of the trapezium = 8cm  

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

To find:-

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.

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)

SOLUTION:-

let the length of one parallel side be x.

then, length of other parallel side = x+5

area=100 cm^2

height=8cm

According to the question:-

1/2 × 8 × (x+x+5) = 100

4 ×(2x+5) =100

8x+20=100

8x = 100-20=80

x = 80/8= 10

hence , one parallel side = 10 cm

other parallel side = (10+5)cm = 15cm

               

                   Hope it helps :D

Answer 2

Given :

• Area of the trapezium = 100 cm²
• Height of the trapezium = 8 cm
• one of the parallel sides is longer than the other by 5 cm.

To Find :

• The parallel sides of the trapezium.

Solution :

Area of trapezium is given by ,

$\\ \: { \underline{\boxed{\red{\bf{Area_{(trapezium)} = \frac{1}{2} \times (a + b) \times h}}}}}$

here,

• a and b are Parallel sides.
• h is height of trapezium.

Substituting the values we have ,

$\\ : \implies \tt \: 100 = \frac{1}{2} \times (a + a + 5) \times 8$

$: \implies \tt\: 100 = \frac{1}{2} \times (2a + 5) \times 8$

$: \implies \tt \: 100 = 4 \times (2a + 6)$

$: \implies \tt \: 2a + 5= \frac{100}{4}$

$: \implies \tt \: 2a + 5= 25$

$: \implies \tt \: 2a = 25-5$

$: \implies \tt\: 2a =20$

$: \implies \tt \: a = \frac{20}{2}$

$: \implies{\underline{\boxed {\pink{\mathfrak{a =10 \: cm }}}}} \: \bigstar$

Then the other parallel side b is ;

$\\ : \implies \tt \: b = a + 5$

$: \implies \tt \: b = 10 + 5 \: cm$

$: \implies{\underline{\boxed {\pink{\mathfrak{b = 15 \: cm}}}}} \: \bigstar$

Hence ,

• The parallel sides of the given trapezium are 15 cm and 10 cm