Question

the length of the parallel sides of trapezium are in the ratio 3:5 and the distance between the two parallel side is 10 cm if the area of trapezium is 120 CM square find the length of the parallel side​

Answer 1

Answer :-

• The length of the sides of trapezium are 9cm and 15cm.

Step-by-step explanation:

To Find :-

• The length of the parallel sides of trapezium

Solution:

Given that,

• The length of the parallel sides of trapezium are in the ratio = 3:5
• The distance between the two parallel sides of trapezium = 10cm.
• Area of trapezium = 120cm².

$\underline{\sf{\large{Assumption:}}}$

Let us assume the length of parallel sides of trapezium as 3x and 5x,

As we know that,

$\bigstar \: \: \boxed{\sf{Area \: of \: trapezium = \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times distance \: between \: them}}$

Hence,

$\bf{\mapsto \: \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times distance \: between \: them = Area} \\ \\ \\ \\ \bf{\mapsto \: \dfrac{1}{2} \times (3x + 5x) \times 10 = 120} \\ \\ \\ \\ \bf{\mapsto \: 1 \times (3x + 5x) \times 10 = 120 \times 2} \\ \\ \\ \\ \bf{\mapsto \: 1 \times (3x + 5x) \times 10 = 240} \\ \\ \\ \\ \bf{\mapsto \: (3x + 5x) \times 10 = 240} \\ \\ \\ \\ \bf{\mapsto \: (3x + 5x) = \dfrac{240}{10}} \\ \\ \\ \\ \bf{\mapsto \: (3x + 5x) = \cancel{\dfrac{240}{10}}} \\ \\ \\ \\ \bf{\mapsto \: (3x + 5x) = 24} \\ \\ \\ \\ \bf{\mapsto \: 8x = 24} \\ \\ \\ \bf{\mapsto \: x = \dfrac{24}{8}} \\ \\ \\ \\ \bf{\mapsto \: x = \cancel{ \dfrac{24}{8}}} \\ \\ \\ \\ \bf{\mapsto \: \red{x = 3}}$

Hence, The value of x is 3. Now, The parallel sides of trapezium are :-

The length of a side which we assumed as 3x :-

$\bf{ \mapsto \: (3x)cm} \\ \\ \bf{ \mapsto \: (3 \times 3)cm} \\ \\ \bf{ \mapsto \: \red{9cm}}$

The length of a side which we assumed as 5x :-

$\bf{ \mapsto \: (5x)cm} \\ \\ \bf{ \mapsto \: (5 \times 3)cm} \\ \\ \bf{ \mapsto \: \red{15cm}}$

Therefore, The length of the sides of trapezium are 9cm and 15cm.

Answer 2

Given :-

• The length of the parallel sides of trapezium are in the ratio 3:5.
• Height of Trapezium = 10cm
• Area of Trapezium = 120cm²

To Find :-

• The length of the parallel sside

Solution :-

⟼ Let the First Parallel side be 3x

⟼ Let the Second Parallel side be 5x

❏ As we know that, Area of Trapezium is given by [ Area = ½ × height × ( sum of parallel sides ) ]

Putting the Values :

➞ Area = ½ × height × (sum of parallel side)

➞ 120 = ½ × 10 × ( 3x + 5x )

➞ 120 = 5 × ( 3x + 5x )

➞ 120 / 5 = ( 3x + 5x )

➞ 24 = ( 3x + 5x )

➞ 24 = 8x

➞ 24 / 8 = x

➞ 3 = x

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Verification :

⟾ Area = ½ × height × (sum of parallel side)

⟾ Area = ½ × 10 × ( 3x + 5x )

⟾ Area = ½ × 10 × ( 3 × 3 + 5 × 3 )

⟾ Area = ½ × 10 × ( 9 + 15 )

⟾ Area = ½ × 10 × 24

⟾ Area = 5 × 24

⟾ 120 = 120

Hence Verified

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Therefore :

• First Parallel Side = 3x = 3 × 3 = 9cm
• Second Parallel Side = 5x = 5 × 3 = 15cm

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