Maths-
General
Easy
Question
In the triangle ABC, angle B = 90 degrees. The internal bisector of the angle B meets AC at D. Given that AB= 3 cm, BC= 4 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
Angle Bisector Theorem: An angle bisector of an angle of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
The correct answer is: Hence, the length of AD is 15/7 cm.
Applying Pythagoras theorem in △ABC
AC2 = AB2 + BC2
AC2 = 32 + 42
AC2 = 25
AC = 5 cm
Applying angle Bisector Theorem
Let the length of AD is x. So the length of CD is AC-AD i.e. 5-x
Final Answer:
Hence, the length of AD is 
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