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Question
The length of a rectangle is twice its breadth . If its length is decreased y 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq. cm . Find the length of the rectangle.
20 cm
25 cm
30 cm
Try your self
ANSWER : 4
Descrption
<pre>Correct answer is 40 cm. Let, breadth x cm & length 2x cm <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Area = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></math> length decreased by 5 cm <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></math> length = 2x - 5 breadth increased by 5 cm <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></math> breadth = x + 5 Area increased by 75 <math xmlns = "http://www.w3.org/1998/Math/MathML"><mi>c</mi><msup><mi>m</mi><mn>2</mn></msup></math> <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo>(</mo><mi>x</mi><mo> + </mo><mn>5</mn><mo>)</mo><mfenced><mrow><mn>2</mn><mi>x</mi><mo> - </mo><mn>5</mn></mrow></mfenced><mo> - </mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo> = </mo><mn>75</mn></math> <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>2</mn><msup><mi>x</mi><mrow><mn>2</mn><mo> </mo></mrow></msup><mo> - </mo><mn>5</mn><mi>x</mi><mo> + </mo><mn>10</mn><mi>x</mi><mo> - </mo><mn>25</mn><mo> - </mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo> = </mo><mn>75</mn></math> <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> 5x - 25 = 75 <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> 5x = 1000 <math xmlns = "http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> x = 20 breadth = 20 cm length = <math xmlns = "http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>×</mo><mn>2</mn></math> cm = 40 cm. Note : Answer is not present in options. </pre>
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