SSC CPO 2022 PYQ — Question 147

The correct answer is Option 3 i.e. 3.76 cm.

We know that,

Pythagoras Theorem

Hypotenuse² = Perpendicular² + Base² 

Now, according to the question

Applying Pythagoras' theorem to the given triangle ABC

We get, AC² = AB² + BC²

⇒ 17² = 8² + BC²

⇒ BC² = 225

⇒ BC = 15

Now, the above triangle ABC can be divided into two right triangles BDA and BDC

Let the length of AD = x and DC = 17 - x

Applying Pythagoras theorem to the two triangles we get,

⇒ AB² = AD² + BD² and BC² = DC² + BD²

From the above equation

⇒ AB² - AD² = BC² - DC²

⇒ 8² - x² = 15² - (17 - x)²

⇒ 64 - x² = 225 - (289 + x² - 34x)

⇒ 64 - 225 + 289 = 34x

⇒ 128 = 34x

⇒ x = 3.76

So, AD = 3.76 cm