Question
In the given figure, find CD, if AB = 5 cm, AC = 10 cm and AD = 13 cm. (Use = 1.73 )
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 CD is 3.35 m
Given AB = 5 cm, AC = 10 cm and AD = 13 cm
Applying Pythagoras theorem in △ABC
AC2 = BC2 + AB2
BC2 = AC2 - AB2
BC2 = 100 - 25
BC = = 5 = 5 1.73 = 8.65 m
Applying Pythagoras theorem in △ABD
AD2 = BD2 + AB2
BD2 = AD2 - AB
BD2 = 169 - 25
BD = = 12 m
Now, BD = CD + BC
CD = BD - BC
CD = 12 - 8.65 = 3.35 m
Final Answer:
Hence, the value of CD is 3.35 m
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