Quadrilateral ABCD is a rectangle such that the length of its diagonals AC, BD are $8 x + 8$ cm and $24 x - 8$ cm respectively. Find the value of $x$ .

1 cm

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2 cm

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3 cm

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4 cm

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Solution

The correct option is A 1 cm
Given,
AC $= 8 x + 8$ cm and BD $= 24 x - 8$ cm

Since Quadrilateral ABCD is a rectangle, its diagonals will be equal.

Now, AC = BD

$\Rightarrow 8 x + 8 = 24 x - 8$

$\Rightarrow 24 x - 8 x = 8 + 8$

$\Rightarrow 16 x = 16$

$\Rightarrow x = 1$ cm

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