Question

The three sides of a triangle are 40 cm, 24 cm and 32 cm. Find the height corresponding to the longest side.

Answer 1

Given:

The three sides of a triangle are 40 cm, 24 cm and 32 cm.

To find:

The height corresponding to the longest side

Solution:

Here we have, a = 40, b = 24 & c = 32

∴ Semi-Perimeter, S =  $\frac{a\:+\:b\:+\:c}{2} = \frac{40\:+\:24\:+\:32}{2} = \frac{96}{2} = 48 \:cm$

Using the Heron's formula, we will find the area of the given triangle, which is as follows:

∴ Area of the given triangle,

= $\sqrt{S\:(S-a)\:(S-b)\:(S-c)}$

= $\sqrt{48\:(48-40)\:(48-24)\:(48-32)}$

= $\sqrt{48\:\times\:8\:\times\:24\:\times\:16}$

= $\sqrt{147456}$

= $384\:cm^2$

Now, we have to find the height corresponding to the longest side of the triangle i.e., 40 cm.

Also, we have the formula of the area of a triangle as,

$\boxed{\bold{Area\:of\:a\:triangle\:=\:\frac{1}{2} \times base\times height}}$

Here, base = longest side of the triangle = 40 cm

Let "h" be the height of the triangle corresponding to the longest side.

On substituting the value of area and base in the formula of the area of a triangle, we get

∴ $384$ = $\frac{1}{2 } \times40\times h$

⇒ $h = \frac{384\:\times\:2}{40}$

⇒ $h = \frac{768}{40}$

⇒ $\bold{h = 19.2\:cm}$

Thus, the height corresponding to the longest side is 19.2 cm.

-------------------------------------------------------------------------------

Also View:

The length of the sides of a triangle are 33cm,44cm and 55cm respectively. Find the area of the triangle and hence find the height corresponding to the side measuring 44cm.

https://brainly.in/question/1101978

Find the area of a triangle whose sides are 34 CM 20 cm and 42 CM then find the length of altitude corresponding to shortest side.

https://brainly.in/question/1404097

Answer 2

Answer:

my uid 1259562931 anyone want alok