Question

Area of square ABCD is 20 sq. units. If A(2, 3) and B(x, 5) then value(s) of x is
(a) 2, –6
(b) –6, 2
(c) 2,6
(d) –2, –6

Answer 1

SOLUTION

CORRECT QUESTION

TO CHOOSE THE CORRECT OPTION

Area of square ABCD is 20 sq. units. If A(2, 3) and B(x, 5) then value(s) of x is

(a) 2 , - 6

(b) - 2 , 6

(c) 2 , 6

(d) - 2 , - 6

EVALUATION

Here it is given that the area of square ABCD is 20 sq. units.

Side of the square = √20 unit

Now it is given that A(2, 3) and B(x, 5) are two points

So by the given condition

$\displaystyle \sf{ }AB = \sqrt{20}$

$\displaystyle \sf{ \implies \sqrt{ {(x - 2)}^{2} + {(5 - 3)}^{2} } = \sqrt{20} }$

$\displaystyle \sf{ \implies {(x - 2)}^{2} + {(5 - 3)}^{2} } = 20$

$\displaystyle \sf{ \implies {(x - 2)}^{2} + {(2)}^{2} } = 20$

$\displaystyle \sf{ \implies {(x - 2)}^{2} + 4 = 20}$

$\displaystyle \sf{ \implies {(x - 2)}^{2} = 16}$

$\displaystyle \sf{ \implies {(x - 2)}^{} = \pm 4}$

Now

x - 2 = 4 gives x = 6

x - 2 = - 4 gives x = - 2

So the values of x are - 2 , 6

FINAL ANSWER

Hence the correct option is (b) - 2 , 6

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Answer 2

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