Question

The sides of all a triangle are in the ratio 5:12:13.If perimeter if triangle is 180 m find area of triangle....???​

Answer 1

Answer:

Required area of this triangle is 1080 m^2.

Step-by-step explanation:

It is given that the sides of a triangle are in a ratio of 5 : 12 : 13, with the perimeter of 180 m.

Let the sides of the triangle are 5a , 12a and 13a,

We know that perimeter of a triangle is the sum of length of its sides.

Thus,

= > Perimeter of this triangle = sum of lengths of its sides

= > 180 m = 5a + 12a + 13a

= > 180 m = 30a

= > 180 / 30 m = a

= > 6 m = a

As we can see, ratio of the sides form pythagorean triplets[ since ( 13 )^2 = ( 12 )^2 + ( 5 )^2 ] , it means that this is a right angled triangle.

From the properties of right angled triangles : -

• Area of triangle = 1 / 2  x base x height

Therefore,

= > Area of this triangle = 1 / 2 x 5a x 12a     [ 13a is hypotenuse ]

= > Area of this triangle = 5a x 6a

= > Area of this triangle = 30 a^2

Substituting the value of a from above,

= > Area of this triangle = 30 x ( 6 m )^2

= > Area of this triangle = 30 x 36 x m^2

= > Area of this triangle = 1080 m^2

Hence the required area of this triangle is 1080 m^2.

Answer 2

Here you go..! Hope it helped.!