Question

$ABC$ is a triangle, right angles at $C$. If $AB=25cm$ and $AC=7cm$, find $BC$.

Answer 1

Since $\Delta ABC$ is right-angled at $C$. Then $AB$ is the hypotenuse.

Now using Pythagorous theorem we get,

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

or. $B{C}^2=A{B}^2-A{C}^2$
or, $B{C}^2={25}^2-7^2$
or, $B{C}^2=(25+7)(25-7)$ [Using identity $a^2-b^2=(a+b)(a-b)$]

or, $B{C}^2=32\times 18$
or, $B{C}^2=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$
or, $BC=\sqrt{\underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{2\times 2}\times \underset{–}{3\times 3}}$

or, $BC=2\times 2\times 2\times 3$

or, $BC=24$

So, $BC=24$ cm