Question

The side of a triangle are at the ratio of 25:14:12 and its perimeter is 510 . Find its sides and area

Answer 1

the perimeter = the sum. of the sides of that triangle

so , the sides are A , B , C

A : B : C : the perimeter

25 : 14 : 12 : 51

a : b : c : 510

so , a = ( 510 * 25 ) / 51 = 250

similarly , b = 140

c = 120

then the area =  √( ( s )(s-a)(s-b)(s-c))

s = half of the perimeter = 255

so the area = 4449.086

Answer 2

Answer:

Required three sides are 250 unit,140 unit and 120 unit.

And area 225√391 square unit.

Step-by-step explanation:

Given,

The side of a triangle are at the ratio of 25:14:12

Let , first side of the triangle be 25x unit.

Second side of the triangle be 14x unit.

and third side of the triangle be 12x unit.

Here we want to find perimeter of the triangle.

But question is how can we find it?

If three sides of a triangle are a,b,c then perimeter of the triangle will be $(a + b + c)$unit .

For example,

Three sides of a triangle are 10 cm,12cm and 15 cm

Then perimeter of the triangle $= (10 + 12 + 15) = 37$cm.

Here sides of the triangle are 25x,14x and 12x.

So perimeter of the triangle is $(25x + 14x + 12x) = 51x$unit.

It is given that perimeter of the triangle is 510 unit.

So according to question,

$51x = 510 \\ x = \frac{510}{51} \\ x = 10$

So, first side of the triangle is (25×10)=250 unit

Second side of the triangle is (14×10)=140 unit

Third side of the triangle is (12×10)=120 unit

We know ,

Area of triangle with three unequal sides $= \sqrt{s(s - a)(s - b)(s - c)}$

Where,

a,b,c are length of three unequal side and

$s = \frac{a + b + c}{2}$

Here,

$s = \frac{250 + 140 + 120}{2} = 255$

Required area

$= \sqrt{255 \times (255 - 250)(255 - 140)(255 - 120)}$

$= \sqrt{255 \times 5 \times 115 \times 135} \\ = \sqrt{17 \times 5 \times 3 \times 5 \times 5 \times 23 \times 5 \times 3 \times 3 \times3} \\ = 5 \times 5 \times 3\times 3 \sqrt{17×23} \\ = 225 \sqrt{391}$square unit.