Question

the area of trapezium is 105 cm² and its height is 7 cm . if one of the parallel sides is longer than the other by 6 cm then find the lengths of two parallel sides .​

Answer 1

To Find:-

• Find the length of two parallel sides.

Given:-

• The area of trapezium is 105 cm²
• It's height is 7 cm.
• If one of the parallel sides is longer than the other by 6 cm.

Solution:-

Let the first side be " x "

The the second side is 6 more then other = x + 6

As we know that:-

$\tt \: Area \: of \: Trapezium = \dfrac { a + b } { 2 } \times h$

Substituting Values:-

$\tt\implies \: 105 = \dfrac { x + x + 6 } { 2 } \times 7$

$\tt\implies \: 105 \times 2 = ( { x }^{ 2 } + 6 )7$

$\tt\implies \: 210 = { 7x }^{ 2 } + 42$

$\tt\implies \: { 7x }^{ 2 } = 210 - 42$

$\tt\implies \: { 7x }^{ 2 } = 168$

$\tt\implies \: { x }^{ 2 } = \dfrac { 168 } { 7 }$

$\tt\implies \: x = \sqrt { 24 }$

$\tt\implies \: x = 5$

Hence,

• $\tt \: First \: \: side \: \: is \: \: 5 cm.$

• $\tt \: Second \: \: side \: \: is \: \: x + 6 = 11 cm.$

Answer 2

Given :-

• Area of Trapezium = 105cm²
• Height of Trapezium = 7cm
• One of the parallel sides is longer than the other by 6 cm

To Find :-

• Lengths of Two parallel sides.

Solution :-

Let First Side be x cm

Then second Side will be x + 6 cm

➟ Area of Trapezium = ½ × height × sum of parallel sides

➟ 105 = ½ × 7 × x + (x + 6)

➟ 105 = ½ × 7 × (x² + 6)

➟ 105 × 2 = 7 × (x² + 6)

➟ 210 = 7x² + 42

➟ 210 - 42 = 7x²

➟ 168 = 7x²

➟ 168/7 = x²

➟ 24 = x²

➟ √24 = x

➟ 5 = x { approx }

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First Side = x = 5cm

Second Side = x + 6 = 5 + 6 = 11cm

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