Question

$△$ABC is right angled at A. If AB = 10 cm and AC = 24 cm,then BC = _________ cm.

• A. 10
• B. 13
• C. 25
• D. 26

Answer 1

The correct option is D

26

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

$B{C}^2={10}^2+{24}^2$

$B{C}^2=100+576$

$B{C}^2=676$

$B{C}^2={26}^2$

ALTERNATE APPROACH :

$B{C}^2={10}^2+{24}^2$

$B{C}^2=(2\times 5{)}^2+(2\times 12{)}^2$

$B{C}^2=2^2(5^2+{12}^2)$

$B{C}^2=2^2\left({13}^2\right)$ .....(5 -12 -13 Pythagoras Triplet)

BC = 26 cm Hence (D)