Question

Side of a triangle are 14:19:25 and it's perimeter is 580m.Find it's area

Answer 1

Answer:

Area of triangle is 1000√174 sqm = 13191 sqm (approx)

Step-by-step explanation:

As the sides of the triangles are in the ratio 14:19:25, we can assign them as:

14x, 19x and 25x.

Given perimeter = 580m

=> 14x + 19x + 25x = 580

=> 58x = 580

=> x = 10

Now, the sides of the triangle are 14x, 19x and 25x

=> Sides of the triangle are: 140, 190 and 250

We can find area of the triangle using Heron's formula

Area of triangle = $\sqrt{S(S-S_{1}) (S-S_{2})(S-S_{3})}$

where $S_{1}$, $S_{2}$ and $S_{3}$ are the three sides and S is the half perimeter

Given: Perimeter of triangle = 580 => S = 290

Area = $\sqrt{290(290-140)(290-190)(290-250)}$

        = √(290)(150)(100)(40)

        = √174000000

        = √174 x √1000000

        = 1000√174

Area of triangle is 1000√174 = 13191 sqm (approx)