Question

The area of trapezium is 200 cm square and it's height is 8 cm. If one of the parallel sides is longer than the other by 6 cm, find the parallel sides.

Answer 1

Answer:

Step-by-step explanation:

Given area : 200 cm sq. ....... (1)

Height : 8 cm

Let 1 parallel side be :x

And 2 parallel side : x +6

Now,

ar. ll gm _ 1÷2 × (sum of ll sides) × height:

1÷2 ×(x + x+6) × 8= 1÷2 ×( 2x

+6) ×8

(x + 3) × 8 = 8x + 24

from (1) : 8x + 24=200

8x = 200-24

x=176 ÷ 8

x=22 cm

So, 1st side = 22 cm

And, 2nd ll side =22+6 = 28

Answer 2

Answer:

22 and 22+6 = 28 cm respv.

Step-by-step explanation:

$\text{Let one side of the trapezium be  x cm. Then, the other side = (x+6) cm}\\\\\text{Given height = 8 cm}\\\\\text{Given area = 200 cm}^2\\\\\text{But, formula for area of trapezium = } \dfrac{1}{2} \times (\text{Sum of \parallel sides}) \times (Height)\\\\\\= \dfrac{(x+x+6) \times (8)}{2}\\\\\\= 2x+6 \times 4\\\\or, \: 4(2x+6) \: cm^2\\\\\text{According to the question,}\\\\4(2x+6) = 200\\\\\implies 2x+6 = 200 \div 4 = 50\\\\\implies 2x = 50 - 6 = 44\\\\\implies x = 44 \div 2$

$\implies x = \large \underline{\boxed{\boxed{\bold{22 \: cm \: and \: 22+6 = 28 \: cm}}}}$

Hope it helps!