Question

If Area of any Triangle is 384 cm' and its sides are in
Ratio 3:4:5 then perimetre of triangle will be?
1. 60cm
2. 48cm
3. 64cm
4. 96cm​

Answer 1

Answer:

4. perimeterof the tringle=96

Answer 2

GIVEN:

Area of the triangle=$384cm^{2}$

The ratio of sides of the triangle is 3:4:5

TO FIND:

The perimeter of the triangle

SOLUTION:

Let the ratio be 3x, 4x, 5x

When it is not mentioned about the type of triangle we are dealing with we use heron's formula

$S=\frac{a+b+c}{2}$

where S is semi-perimeter of the triangle

a, b, c is the side length of the triangle

$S=\frac{3x+4x+5x}{2}\\S=\frac{12x}{2} \\S=6x$

Now for the area of the triangle

$Area=\sqrt{s(s-a)(s-b)(s-c)} \\\\384=\sqrt{6x(6x-3x)(6x-4x)(6x-5x)}\\384=\sqrt{6x*3x*2x*x} \\384=\sqrt{36x^{4} } \\384=6x^{2} \\x^{2} =64\\x=8$

Since the value of x=8,

the perimeter of the triangle =3x+4x+5x

                                               =12x

                                               =12*8

                                               =96cm

Hence, the perimeter of the triangle is 96 cm which is an option (4)