Question

The lengths of a triangle are $6cm,8cm$ and $10cm$. Then the length of perpendicular from the opposite vertex to the side whose length is $8cm$ is:

• A. 5 cm
• B. 2 cm
• C. 6 cm
• D. 4 cm

Answer 1

The correct option is B. $6cm$

Let $\Delta ABC$ be a triangle such that $AB=6cm,BC=8cm$ and $AC=10cm$

Now, if $\Delta ABC$ satisfy the Pythagoras Theorem, then $AC$ will be the hypotenuse and angle at point $B$ will be ${90}^{\circ }$.

LHS: $A{B}^2+B{C}^2$

$=6^2+8^2$

$=100$

RHS: $A{C}^2={10}^2=100$

Therefore, $A{B}^2+B{C}^2=A{C}^2$ and thus $\Delta ABC$ is a right angled triangle at point $B$

Therefore, perpendicular at side $BC=8cm$ is $AB=6cm$.