Q. 205.0( 1 Vote )

In a , perpendicular AD from A on BC meets BC at D. If BD = 8 cm, DC = 2 cm and AD = 4 cm, then
A. is isosceles

B. is equilateral

C. AC = 2 AB

D. is right-angled at A.

Answer :

Given in ΔABC, AD BC, BD = 8 cm, DC = 2 cm and AD = 4 cm.



We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.


Now, in right triangle ADC,


AC2 = AD2 + DC2


AC2 = (4)2 + (2)2


= 16 + 4


AC2 = 20 … (1)


In ΔADB,


AB2 = AD2 + BD2 = 42 + 82 = 16 + 64


AB2 = 80 … (2)


Now, in ΔABC,


BC2 = (CD + DB)2 = (2 + 8)2 = 102 = 100


And AB2 + CA2 = 80 + 20 = 100


AB2 + CA2 = BC2


Hence, ΔABC is right angled at A.

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