Question

The sides of the triangle are in the ratio 5 : 12 : 13 the perimeter is 150 cm the area of the triangle is

Answer 1

Answer:

Let the sides be 5x, 12x and 13x

A/Q, 5x + 12x + 13x = 150 cm

=> 30x = 150

=> x = 150/30

=> x = 5 cm

Therefore, 5x = 25 cm, 12x = 60 cm and 13x = 65 cm

Area of triangle = ½ × 25 × 60

= 750 cm²

*Didn't use Heron's formula as the sides of the triangle are Pythagorean Triplets

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Answer 2

Perimeter of the triangle is 150 cm
The sides are in a ratio of 5:12:13
On dividing 150 in the ratio 5:12:13
We get a= 5x
B= 12x
C=13x
The sum of all sides is the perimeter
So
5x + 12x+13x=150 cm
30x =150cm
X=5 cm
So the sides are a= 25 b=60 and c=65
Apply Heron’s formula to find the area of the triangle
Root of s*(s-a)(s-b)(s-c)
Where s=a+b+c/2
S=75cm
Root of 75*75-25*75-60*75-65
=Root of 75*50*15*10
=750cm^2

So the area of the triangle is 750cm^2