The length of a rectangle is twice its width. If its length is decreased by 5cm and the width is increased by 5cm, the area of the rectangle is increased by 75cm2. Find the perimeter of the original rectangle.
A
120cm
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B
None of the above
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C
240cm
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D
210cm
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Solution
The correct option is A120cm Let the width of the original rectangle be x. ⇒ Length of the original rectangle =2x
Now,
New length of the rectangle =2x−5
New width of the rectangle =x+5
New area of the rectangle = Original area of the rectangle +75 ⇒(2x–5)×(x+5)=2x×x+75 ⇒2x2+10x–5x–25=2x2+75 ⇒5x−25=75 ⇒5x=100 ⇒x=20cm
Now,
Perimeter of the original rectangle =2(2x+x)=2(3x)=6x=6×20=120cm