Question

the area of a trapezium is 224 square and its height is 14 cm if one of the parallel side is longer than other by 8 cm find the length of two parallel sides​

Answer 1

Answer:

The lengths of the parallel sides are $20 cm$ and $12 cm$.

Step-by-step explanation:

Area of a trapezium is $\frac{1}{2} . (a + b) . h$ where, a and b are the lengths of the parallel sides and h is the height.

according to the problem:

$a - b = 8$  . . . . . . . . . . . . . . . . . .  (i)

and, $\frac{1}{2} . (a + b) . 14 = 224$

$(a + b) = \frac{224}{7} = 32$ . . . . . . . . . . .  (ii)

Adding equation (i) and (ii):

$2a = 40$

∴ $a = 20$

From equation (ii), $b = 32 - a = 32 - 20 = 12$

Therefore, the lengths of the parallel sides are $20 cm$ and $12 cm$.

Answer 2

Given -

• Area of trapezium = 224cm²

• Height = 14cm

• Parallel side is longer than other by 8cm

To find -

• Length of two parallel sides.

Solution -

Let -

Parallel side be termed as x

so,

2nd side will be termed as x + 8

Now -

Area = $\sf\dfrac{a + b}{2\times h}$

$\longmapsto$ 224 = $\sf\dfrac{x + x + 8}{2\times h}$

$\longmapsto$ 224 = $\sf\dfrac{2x + 8}{2\times14}$

$\longmapsto$ 224 = 7(2x + 8)

$\longmapsto$ 224 = 14x + 56

$\longmapsto$ 224 - 56 = 14x

$\longmapsto$ 168 = 14x

$\longmapsto$ = $\sf\cancel\dfrac{168}{14}$

$\longmapsto$ = 12cm

So -

1st parallel side = 12cm

2nd parallel side = x + 8 = 12 + 8 = 20cm

$\therefore$ The length of two parallel sides are 12cm and 20cm

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