Question

The hypotenuse $AC$ of a right-angled triangle $ABC$ is $10cm$ and $AB=6cm$. Find $BC$.

Answer 1

We use Pythagoras' theorem that the sum of the squares on two legs of a right angled triangle is equal to the square on the hypotenuse.

Thus if $ABC$ is a right angled triangle with $\angle B={90}^o$,

then $AB,BC$ are its legs, $AC$ is its hypotenuse.

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

We are given $AC=10cm$. Suppose $AB=6cm$.

We have to find $BC$. Writing $AC=b,AB=c$ and $BC=a$,

we have $a^2+c^2=b^2$, where $b=10,c=6$. Hence

$a^2=b^2-c^2=(b-c)(b+c)=(10-6)(10+6)=4\times 16=64$

We obtain $a=\sqrt{64}=8cm$.