If ABCD is a rectangle. If the diagonals are of the length (8x - 9) cm and (3x + 6) cm, then find the length of the diagonal.

3 cm

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10 cm

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15 cm

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18 cm

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Solution

The correct option is C 15 cm

ABCD is a rectangle. Hence the lengths of the diagonals are equal.
$\Rightarrow (8 x - 9) = (3 x + 6) = 8 x - 9 = 3 x + 6 = 8 x - 3 x = 6 + 9 = 5 x = 15 \Rightarrow x = \frac{15}{5} = 3$

$8 x - 9$ is the length of the diagonal.
$\Rightarrow 8 \times 3 - 9 = 24 - 9 = 15$

$∴$ The length of the diagonal is 15 cm.

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