# ABC is a triangle, right angled at $C$. If $AB = 25cm $ and \[AC = 7cm\], find

BC.

Answer

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Hint: Draw the diagram of the right triangle to find out which of the three sides is

the hypotenuse, base or perpendicular. Using Pythagoras theorem, find the unknown side.

We are given that the $ABC$ is a triangle, right angled at $C$

Then, $AB$ is the hypotenuse,$AC$ is the base and $BC$ perpendicular

Now, according to the Pythagoras theorem we know that,

${({\text{hypotenuse}})^2} = {(base)^2} + {(perpendicular)^2}$

Therefore, using this we get,

${({\text{AB}})^2} = {(AC)^2} + {(BC)^2}$

Now after substituting the given values we get,

$ \Rightarrow {({\text{7}})^2} = {(25)^2} + {(BC)^2}$

$ \Rightarrow {(BC)^2} = {(25)^2} - {({\text{7}})^2}$

$ \Rightarrow {(BC)^2} = 625 - 49$

$ \Rightarrow {(BC)^2} = 576$

$ \Rightarrow BC = 24$

$\therefore BC = 24cm$

So, this is the required solution.

Note: In order to solve these types of questions, simply put the given values of the sides of

the right triangle in the Pythagoras theorem and evaluate it to obtain the required solution.

the hypotenuse, base or perpendicular. Using Pythagoras theorem, find the unknown side.

We are given that the $ABC$ is a triangle, right angled at $C$

Then, $AB$ is the hypotenuse,$AC$ is the base and $BC$ perpendicular

Now, according to the Pythagoras theorem we know that,

${({\text{hypotenuse}})^2} = {(base)^2} + {(perpendicular)^2}$

Therefore, using this we get,

${({\text{AB}})^2} = {(AC)^2} + {(BC)^2}$

Now after substituting the given values we get,

$ \Rightarrow {({\text{7}})^2} = {(25)^2} + {(BC)^2}$

$ \Rightarrow {(BC)^2} = {(25)^2} - {({\text{7}})^2}$

$ \Rightarrow {(BC)^2} = 625 - 49$

$ \Rightarrow {(BC)^2} = 576$

$ \Rightarrow BC = 24$

$\therefore BC = 24cm$

So, this is the required solution.

Note: In order to solve these types of questions, simply put the given values of the sides of

the right triangle in the Pythagoras theorem and evaluate it to obtain the required solution.

Last updated date: 29th Sep 2023

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