Question

QUESTION:A rectangular lot has an area of 132m² and a perimeter of 46m.which of the following quadratic equation illustrates the given situation?

A.x²-23x+132=0
B.x²+23x+132=0
C.x²+46x-132=0
D.x²-46x+132=0

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Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A rectangular lot has an area of 132m² and a perimeter of 46m.which of the following quadratic equation illustrates the given situation

A. x² - 23x + 132 = 0

B. x² + 23x + 132 = 0

C. x² + 46x - 132 = 0

D. x² - 46x + 132=0

EVALUATION

Let length = x meter and breadth = y meter

Here it is given that the perimeter is 46m

So by the given condition

2 ( x + y ) = 46

⇒ x + y = 23

⇒ y = 23 - x

⇒ Breadth = 23 - x

Now the rectangular lot has an area of 132m²

So by the given condition

Length × Breadth = 132

⇒ x( 23 - x ) = 132

⇒ 23x - x² = 132

⇒ x² - 23x + 132 = 0

FINAL ANSWER

Hence the correct option is

A. x² - 23x + 132 = 0

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