Question

If the hypotenuse of a right angled triangle is 13 cm, what will be the other side lengths?

• A. $11$ cm and $4\sqrt{3}$ cm
• B. $9$ cm and $2\sqrt{3}$ cm
• C. $11$ cm and $2\sqrt{3}$ cm
• D. $9$ cm and $4\sqrt{3}$ cm

Answer 1

The correct option is A $11$ cm and $4\sqrt{3}$ cm

In right angled triangled triangle the side lengths form a Pythagorean triplet.

$\Rightarrow {\text{Hypotenuse}}^2={\text{Base}}^2+{\text{height}}^2$
$\Rightarrow {13}^2={\text{Base}}^2+{\text{height}}^2$
$\Rightarrow 169={\text{Base}}^2+{\text{height}}^2$

We need to check the option which satisfy this equation.

Checking option A,
${11}^2+(4\sqrt{3}{)}^2=121+(16\times 3)$
$=121+48$
$=169$

The correct answer is option A.