Question

find AD in the following figure if BC = 5cm , AB = 3 cm , and AC = 4cm​

Answer 1

I hope it will help you

Answer 2

The length of AD is $2.4\,\,{\rm cm}$.

Given:

A triangle with sides, BC = 5cm , AB = 3 cm, and AC = 4cm​.

To Find:

The length of AD.

Solution:

Consider the figure.

The area of the triangle is given by, $\frac{1}{2}\times {\rm base}\times {\rm altitude}$.

Compute the area of triangle ABC considering the base as 3 cm and altitude as 4 cm. Let $A_1$ be that area.

$A_1=\frac{1}{2}\times 3\times 4\\=6\,\,\,{\rm cm^2}$

Compute the area of triangle ABC considering the base as 5 cm and altitude as AD. Let $A_2$ be that area.

$A_2=\frac{1}{2}\times 5\times {\rm AD}$

Both $A_1$ and $A_2$  are the area of triangle ABC. So their area can be equated to find AD.

Equate the area of both the triangle and find AD.

$\frac{1}{2}\times 5\times {\rm AD}=6\,\,\,{\rm cm^2}\\{\rm AD}=\frac{12}{5}\,\,{\rm cm} \\=2.4\,\,{\rm cm}$

Thus, the length of AD is $2.4\,\,{\rm cm}$.