ΔABC is right-angled at B and D is a point on AC such that BD is perpendicular to AC. If BD = 6 cm and AD = 3 cm, then what will be the length of AC?

15 cm

We know that,

P² + b² = h²

We have,

BD = 6 cm

AD = 3 cm

According to the given data,

AB² = AD² +  BD²

= AB² = 3² +  6²

= AB² = 45

We also know that,  AD = \(\frac{AB^2}{AC}\) 

= 3 = \(\frac{45}{AC}\)

= AC = 15 cm