Question

$△$ABC is right angled at A. If AB = 12 cm and AC = 16 cm, then BC = ____________ cm.

• A. 10
• B. 15
• C. 20
• D. 25

Answer 1

The correct option is C

20

In a right angle triangle, Pythagoras Theorem states that the sum of the squares of the sides containing the right angle is equal to the square of the hypotenuse.

Therefore, $B{C}^2=A{B}^2+A{C}^2$

$B{C}^2={12}^2+{16}^2$

$B{C}^2=144+256$

$B{C}^2=400$

$B{C}^2={20}^2$

$BC=20cm$

ALTERNATE APPROACH :

$B{C}^2={12}^2+{16}^2$

$B{C}^2=(4\times 3{)}^2+(4\times 4{)}^2$

$B{C}^2=4^2(3^2+4^2)$

$B{C}^2=4^2\left(5^2\right)$ ........(3 -4 -5 Pythagoras Triplet)

$BC=20cm$

Hence (C)