Question

The side of a triangle plot are in the ratio 3 ratio 5 ratio 4 and the perimeter is 48 0 m find its area​

Answer 1

Answer:

19200 root 3 meter square

Explanation:

Let the sides be 3x,5x and 4x

Perimeter= 480m

3x+5x+4x= 480

12x = 480

x = 480/12

x = 40m

Then the length of the sides are

a = 3x = 3*40 = 120m

b = 5x = 5*40 = 200m

c = 4x = 4*40 = 160m

semi perimeter (s) = 480/2 = 240m

Area = root s (s-a) (s-b) (s-c)

area = root 240 (240-120) (240-200) (240-160)

area = root 240 * 120 * 40 * 80

area = 100 root 24 * 12 * 4 * 8

area = 100 root 2*2*2*2*3*3 * 2*2*3 * 2*2 * 2*2*2

area = 100 * 2*2*3*2*2*2*2 root 3

area = 19200 root 3 m square

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Ratio of sides of triangle = 3 : 5 : 4

• Perimeter of triangle = 480

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What are the sides of the given triangle?

Formula to be used :-

• Perimeter of triangle = sum of all sides

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

As per question :-

Ratio of sides of triangle = 3 : 5 : 4

Let the sides of triangle be 3x , 5x and 4x.

We know,

Perimeter of triangle = sum of all sides

Given that,

Perimeter of triangle is = 480

According to the question :-

⟶ 3x + 5x + 4x = 480

⟶ 12x = 480

⟶ x = 40

_______________________________________________

Hence,

1st side = 3x = 3 × 40 = 120 m

2nd side = 5x = 5 × 40 = 200 m

3rd side = 4x = 4 × 40 = 160 m

Therefore, all sides of the given triangles are 120 m, 200 m and 160 m.

______________________________________________

Verification :-

Given that,

⟶ Perimeter of triangle = 480

⟶ 120 + 200 +160 = 480

⟶ 480 = 480

L.H.S = R.H.S

(Verified)