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 $x$ .

2 cm

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4 cm

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1 cm

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3 cm

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Solution

The correct option is C 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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Quadrilateral ABCD is a rectangle such that the length of its diagonals AC, BD are 8x+8 cm and 24x –8 cm respectively. Find the value of x.

The correct option is C 1 cmGiven, AC =8x+8 cm and BD =24x−8 cm Since Quadrilateral ABCD is a rectangle, its diagonals will be equal. Now, AC = BD ⇒8x+8=24x−8 ⇒24x−8x=8+8 ⇒16x=16 ⇒x=1 cm

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 $x$ .

The correct option is C 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