If the area of a rectangle whose length is 5 units more than twice its width is 75 sq units then wha...........

Quantitative Aptitude ( CCS) Mensuration 2D

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If the area of a rectangle whose length is 5 units more than twice its width is 75 sq units, then what is the width ?

3 units

5 units

7 units

10 units

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Explanation:

Given, Area of rectangle = 75 sq unit
Let width (b) of the rectangle be x unit.
Then, length (l) of the rectangle be (2x + 5) unit.
∴ Area of rectagle = l × b
⇒ 75 = (2x + 5) × x
⇒ 2x² + 5x – 75 = 0
⇒ 2x² + 15x – 10x – 75 = 0
⇒ x(2x + 15) – 5(2x + 15) = 0
⇒ (x – 5) (2x + 15) = 0
⇒ x = 5 units (? 2x + 15 = 0, x cannot be negative)
Hence, width of the rectangle be 5 units.