Maths-
General
Easy
Question
In right angled triangle ∠ABC, ABC = 90° and CD = 2BD. If AB = 12 cm and AC = 15 cm, find AD.
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: Hence, the value of AD is 3√17 cm
Given CD = 2BD, AB = 12 cm and AC = 15 cm
Applying Pythagoras theorem in △ABC
AC2 = AB2 + BC2
152 = 122 + BC2
BC2 = 225 - 144
BC2 = 81
BC = 9 cm
AC2 = AB2 + BC2
Now, BC = BD + CD
BC = BD + 2BD
3BD = 9 cm
BD = 3 cm
Applying Pythagoras theorem in △ABD
AD2 = AB2 + BD2
AD2 = 122 + 32
AD2 = 153
Final Answer:
Hence, the value of AD is 3
cm
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