Question

In the adjoining figure, ABC is right angled at B. Its legs are 8 cm and 6 cm. Find the length of perpendicular BN on the side AC.

Answer 1

:::YOUR ANSWER IS IN THE FORM OF PICTURE :::

Answer 2

Answer:

BN = 4.8 cm

Step-by-step explanation:

In ΔABC, Taking BC as a base and AB as height

$\text{Area of triangle ABC = }\frac{1}{2}\times Base\times Height\\\\\implies Area=\frac{1}{2}\times BC\times AB\\\\\implies Area=\frac{1}{2}\times 6\times 8\\\\\bf\implies Area = 24\thinspace{ cm^2}$

By using Pythagoras theorem in triangle ABC,

AC² = BC² + AB²

AC² = 6² + 8²

AC² = 36 + 64

AC² = 100

⇒ AC = 10 cm

Now, in triangle ABC, taking AC as base and BN as height :

$\text{Area of triangle ABC = }\frac{1}{2}\times Base\times Height\\\\\implies Area=\frac{1}{2}\times AC\times BN\\\\\implies 24=\frac{1}{2}\times 10\times BN\\\\\implies BN = \frac{2\times 24}{10}\\\\\bf\implies BN = 4.8\text{ cm}$