Question

the length of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 120cm.Find its area.

Answer 1

let the sides be 3x, 4x, and 5x cm long
3x + 4x + 5x = 120
12x = 120
x = 10
so 3x = 30
4x = 40
5x = 50
so the sides are 30cm, 40cm, and 50cm
a = 30, b = 40, c = 50
s = ½p = 60
by Heron's formula,
area = √[s(s-a)(s-b)(s-c)]
= √[60(60-30)(60-40)(60-50)]
= √[60*30*20*10]
= √360000
= 600
therefore the area of the triangle is 600cm²

Answer 2

Step-by-step explanation:

Let the nos. be: 3x, 4x and 5x .

So,

3x+4x+5x=120

OR

x(3+4+5)=120

Now,

x = 120 ÷ (3+4+5)

x = 120 ÷ 12

x=10

So, from here as our value for x is 10 ,

We will multiply 10 by the ratio nos.

So,

3×10=30unit

4×10=40unit

5×10=50unit

Now we will use heron's formula for the area

That is :-

=√[s(s-a)(s-b)(s-c)] where s=1/2 of perimeter that is 1/2×120=60

So,

=√[60(60-30)(60-40)(60-50)]

=√[60×30×20×10]

=√[360000]

=600

So, 600 unit ^2 is the area of the triangle.