Question

If the sides of a triangle are in the ratio 15:12:3 and its perimeter is 450,find the area

Answer 1

Answer:

perimeter of triangle = sum of all sides

let the ratio numbers = 15x , 12x , 3x

450. = 15x + 12x + 3x

450 = 30x

x = 15

15x = 15*15 = 225

12x = 12*15=180

3x = 3*15 = 45

area of triangle = 1/2 * b * h

= 1/2* 45 * 225

= 5062.5

hope it helps you

Answer 2

Given

Sides of ∆ are in ratio = 15 : 12 : 3

Perimeter of ∆ = 450 units.

To Find

Area of triangle

Solution

Let the sides of ∆ be 15y, 12y & 3y.

We know that,

➥ Perimeter of ∆ = Sum of 3 sides.

Putting values :

➝ 15y + 12y + 3y = 450

➝ 30y = 450

➝ y = 450/30

➝ y = 15

Finding sides if triangle :

⟼ First side = 15y = 15(15) = 225 units.

⟼ Second side = 12y = 12(15) = 180 units.

⟼ Third side = 3y = 3(15) = 45 units.

Now finding semi-perimeter of ∆ :

➾ Semi-perimeter(s) = Perimeter/2

➾ Semi-perimeter(s) = 450/2

➾ Semi-perimeter (s) = 225 units.

Using Heron's formula for finding area of ∆

➥ √[s(s - a)(s - b)(s - c)]

Putting values we get :

➙ Area of∆ = √[225(225 - 225)(225 - 180)(225 - 45)]

➙ Area of ∆ = √[225 × 0 × 45 × 180]

➙ Area of ∆ = √0

➙ Area of ∆ = 0 unit²

[Note : Here, the three verticles of triangle are collinear, so it's area = 0 ]

Therefore,

Area of triangle = 0 unit² .