Question

the sides of a triangle are in the ratio 5:4:3. if its perimeter is 96 cm, using herons formula, find the area of triangle.

Answer 1

Hey friend,
Here is the answer you were looking for:
$given \\perimeter = 96cm \\ \\ let \: the \: first \: side \: be \: 5x \\ the \: second \: side \: be \: 4x \\ and \: the \: third \: side \: be \: 3x \\ \\ perimeter = 96 \\ \\ a + b + c = 96 \\ \\ 5x + 4x + 3x = 96 \\ \\ 12x = 96 \\ \\ x = \frac{96}{12} \\ \\ x = 8 \\ \\ first \: side \: \\ 5x \\ = 5 \times 8 \\ = 40 cm\\ \\ second \: side \\ = 4x \\ = 4 \times 8 \\ = 32 cm\\ \\ third \: side \\ = 3x \\ = 3 \times 8 \\ = 24 cm\\ \\ semi - primeter = \frac{perimeter}{2} \\ \\ s = \frac{96 }{2} \\ \\ s = 48 \\ \\ heron \: s \: formula \\ = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{48(48 - 40)(48 - 32)(48 - 24)} \\ \\ = \sqrt{48(8)(16)(24)} \\ \\ = \sqrt{48 \times 8 \times 16 \times 24} \\ \\ = \sqrt{147456} \\ \\ = 384 {cm}^{2}$


Hope this helps!!!!

@Mahak24

Thanks..
☺☺

Answer 2

Heya ,

Here's ur answer ,

The perimeter of given triangle =96 cm

The sides of triangle are in ratio 5:4:3 ,

Let x be the common multiple of the sides ,

5x, 4x,3x

The perimeter of triangle = sum of all sides of triangle
96=5x+4x+3x
96=12x
96÷12=x
x=8

The side of triangle are ,

5x=5×8=40
4x=4×8=32
3x=3×8=24


Let ,
a =40
b=32
c=24


The area of triangle by herons formula ,

s
= a+b+c÷2
=40+32+24÷2
=96÷2
=48

A=
$\sqrt{s(s - a)(s - b)(s - c)}$
=
$\sqrt{48(48 - 40)(48 - 32)(48 - 24)}$

=
$\sqrt{48 \times 8 \times 16 \times 24}$
=
$\sqrt{147456}$

=384 square cm


The area of triangle =384 square cm


Hope it helps you !