In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6cm, CD = 5cm, then find the value of AB2 + BD2 (in cm).
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 96
Given:
ABC is a right angled triangle with BD perpendicular to the hypotenuse AC.
AD = 6cm, CD = 5cm
Concept used:
ABC is a right angled triangle at B and BD is perpendicular to AC.
So, ΔABD ∼ ΔACB ∼ ΔBCD
We know that, BD2 = AD × DC ------ (1)
AB2 = AB × AC ----- (2)
Calculations:
Using equation (1), we get
BD2 = AD × DC
⇒ BD2 = 6 × 5 = 30
Using equation (2), we get
AB2 = AB × AC
⇒ AB2 = 6 × (AD + CD)
⇒ AB2 = 6 × (6 + 5)
⇒ AB2 = 6 × 11 = 66
Now, the value of AB2 + BD2 = 66 + 30 = 96 cm