Question

X
In a right angle triangle ABC right angled at B, if AB = 5 cm, AC = 13 cm, then BC is

Answer 1

Answer: 12cm

Step-by-step explanation:

We need to use Pythagoras theorem, which is

$bas^{2} + per^{2} = hyp^{2}$

which is, base squared added to perpendicular squared is the hypotenuse squared. This is always true in any kind of right angled triangle.

In this case, the right angle is at B, as given in the question. So, AC (13cm) is the hypotenuse. AB is 5cm. So, after re-arranging, we can say that

$BC^{2} = AC^{2} - AB^{2}$

$BC^{2} = 13^{2} - 5^{2}$

=169 - 25

=144

$BC^{2} = 144$

$BC = \sqrt{144}$

BC = 12cm

Hope it helps!!

Answer 2

Given,

The right angled triangle $ABC$

In the given triangle, the right angle is at $B$

Then the hypotenuse side will be $AC$

The length of $AB$ is $5cm$

The length of $AC$ is $13cm$

Let the length of $BC$ be $x$

By using Pythagorean theorem

$AC^{2} =AB^{2} +BC^{2}$

$13^{2} =5^{2} +x^{2}$

$169=25+x^{2}$

Taking  $x$ term to LHS and constant terms to RHS

We get,

$x^{2} =169-25$

$x^{2} =144$

$x=\sqrt{144}$

$x=12$

Therefore, the length of the other side $BC$ is $12cm$