Question

the area of a triangle is 150 cm^2 and it s sides are in the ratio 3:4:5 what is its perimeter

Answer 1

Answer:

Let the sides be 3x,4x,5x respectively

Here all three sides are different

that is it's a scalene triangle

so we've to find the answer using Heron's Formula

that is

Area=

$\sqrt{{s} (s - a) (s - b) (s - c)}$

where s= Perimeter/2=Semi Perimeter

here s=

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

therefore s=6x

we've to substitute all the values According to the equation

now the equation is

$\sqrt{{6x} (6x - 3x) (6x- 4x) (6x - 5x)} \\ 150 = \sqrt{6x(3x)(2x)(x)} \\150 = {36x}^{4}$

and now here we know

36=6²

therefore using 6x²

that is

$150 = \sqrt{ {6x}^{2} \times {6x}^{2} }$

here we got 6x² as common

so taking it out of root

$150 = {6x}^{2} \\ {x}^{2} = \frac{150}{6} \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = 5$

and now we've to substitute value of x to the sides

that is

3x=3×5=15

4x=4×5=20

5x=5×5=25

we know

perimeter of a triangle= sum of all sides

that is

perimeter=15+20+25

perimeter=60

therefore the perimeter is 60cm