CBSE Class 10 Answered

In triangle ABC,

From Pythagoras theorem, AC² = AB² + BC²   

                                                 ⇒ AC = 13.

Let NM = p, Then BP = 5 -p

In triangle ANM,

AN² = AM² + NM²  

         = x² + p²

So, AN = (x² + p²)

BN = 13 - (x² + p²)

In triangle BOM,

 BN² = NP² + BP²  

(13 - (x² + p²))² = (12 -x)² + (5 - p)²

169 + x² + p² - 26(x² + p²) = 144 + x² - 24x + 25 + p² - 10p

On solving, we get p = (5/12)x

y = MN + NP = p + 12 - x

                       = (5x/12) + 12 - x

                       = (144-7x)/12

So 'c' is the correct option.