Question

Solve : the question of the image

Answer 1

Answer:

$\bold{30\ \&\ 10}$

Step-by-step explanation:

$Here, \\ \\ OA \times OB = CO \times DO \\ \\ Let\ OA\ be\ (40 - x)\ cm. \\ \\ OA \times OB = (40 - x)x \\ \\ CO \times DO = 15 \times 20 = 300 \\ \\ \\ (40 - x)x = 300 \\ \\ = 40x - x^2 = 300$

$(40x - x^2)(-1) = 300 \times (-1) \\ \\ = x^2 - 40x = -300 \\ \\ x^2 - 40x + 400 = -300 + 400 \\ \\ = (x - 20)^2 = 100 \\ \\ \\ x - 20 = \sqrt{100} \ \ \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ \ \ x - 20 = -\sqrt{100} \\ \\ = x - 20 = 10 \ \ \ \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ \ \ x - 20 = -10 \\ \\ x = 10 + 20 = \bold{30} \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ \ \ x = -10 + 20 = \bold{10}$

$\\ \\ \\ \therefore\ OB = \bold{30\ cm} \ \ \ \ ; \ \ \ \ OA = \bold{40 - 30 = 10\ cm} \\ \\ OR \\ \\ OB = \bold{10\ cm} \ \ \ \ ; \ \ \ \ OA = \bold{40 - 10 = 30\ cm} \\ \\ \\ \therefore\ The\ possible\ values\ of\ x\ are\ \bold{30\ \&\ 10}.$

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