Question

The area of trapezium is 60 cm² and the distance between its parallel sides is 12 cm. If difference between the length of parallel sides is 4 cm, find the length of its parallel sides? ​

Answer 1

Step-by-step explanation:

Answer:-

Given that:-

• The area of trapezium is 60 cm²
• Height of the trapezium is 12 cm
• Difference in the length of parallel side 4 cm

To find:-

Parallel sides measures

Let's Do!

Formula to be applied is:-

$\boxed{\sf{ Area \ of \ Trapezium = \dfrac{1}{2} \times (Sum \ of \ Parallel \ sides) \times Height}}$

• Area of trapezium and height is given
• If we consider the value of one side as x, so other is y.
• x - y = 4 is the equation then. (1)

$\boxed{\sf{60 = \dfrac{1}{2} \times (x + y) \times 12}}$

$\sf{120 = (x + y) \times 12}$

$\sf{10 = (x + y) }$ Equation (2)

Adding (1) and (2)

$\sf{x - y + x + y = 4 + 10}$

$\sf{ 2x = 14}$

$\implies \sf{ x = 7 \ cm}$

Now,

$\implies \sf{ x - y= 4}$

$\sf{ 7 - y= 4}$

$\implies \sf{ y= 3 \ cm}$

Answer 2

Here, as per the provided question we are asked here to find the length of its parallel sides ? –

GIVEN :

• The area of the trapezium = 60cm²

• The distance between its parallel sides = 12cm

• Difference between the length of parallel sides = 4cm

TO FIND :

• The length of its parallel sides = ?

STEP-BY-STEP EXPLANATION :

Now, we will have to apply an appropriate formula –

Formula Used :

• Area of trapezium = 1/2 × (Sum of parallel sides) × height

Therefore, Here we will have to substitute the values as per the provided formula –

$⟹ \: 60 = \frac{1}{2} \times ( \rm {x + y}) \times 12$

$⟹ \: 120 = ( \rm {x + y}) \times 12$

$⟹ \: 10 = ( \rm {x + y})$

Now, we'll have to add the equations :

$⟹ \rm {x - y} \: + \rm {x \: + y} = 4 \: + 10$

$⟹ \: 2 \rm {x} = 14$

$⟹ \rm {x} = 7 \rm {cm}$

Now, we will have to find the length of its parallel sides –

$⟹ \rm {x - y} = 4 \\ ⟹ \: 7 - \rm {y} = 4 \\ ⟹ \rm {y} = 3 \rm {cm}$

Hence, the length of its parallel sides = 3cm.