Question

If hypotenuse of a right angled triangle is $5cm$ and its remaining sides are in the ratio of $1:2$, then find the volume of sides.

Answer 1

Given: $△ABC$ is a right angled triangle.
Hypotenuse $AC=5cm$
and $AB:BC=1:2$
$\Rightarrow$ $AB=1x,BC=2x$

In right angled $△ABC$,

By pythagoras theorem
${AC}^2={AB}^2+{BC}^2$
$\Rightarrow 5^2={\left(1x\right)}^2+{\left(2x\right)}^2$
$\Rightarrow 25=x^2+4x^2$
$\Rightarrow 25=5x^2$
$\Rightarrow x=\sqrt{5}$
Hence, $AB=1x=1\times \sqrt{5}=\sqrt{5}cm$
$BC=2x=2\times \sqrt{5}=2\sqrt{5}cm$