In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm, then find the value of $AB^2+ BD^2$ (in cm).
Answer & explanation
Correct answer: option 2
According to the concept,
\( {BD }^{2 } \) = AD x DC
⇒ \( {BD }^{2 } \) = 6 x 5
⇒ \( {BD }^{2 } \) = 30
According to the concept
\( {AB }^{2 } \) = AD x AC
⇒ \( {AB }^{2 } \) = 6 x (AD + CD)
⇒ \( {AB }^{2 } \) = 6 x (6 + 5)
⇒ \( {AB }^{2 } \) = 6 x 11
⇒ \( {AB }^{2 } \) = 66
Now, \( {AB }^{2 } \) + \( {BD }^{2 } \) = 30 + 66 = 96
Therefore, \( {AB }^{2 } \) + \( {BD }^{2 } \) is 96.