Question

The perimeter of a triangular field is 540 m and its sides are the ratio 25:17:12. Find the area of the triangle.

Answer 1

Hello! !!

Here's the Answer :


$<b><i> =>Let the sides be 25x , 17x and 12x.$

Perimeter of the triangle = 540 m
a + b + c = 540
25x + 17x + 12x = 540
54x = 540
x = 540 /54
x = 10

=>Sides
a = 25x
= 25 × 10
= 250

b = 17x
= 17 × 10
= 170

c = 12x
= 12 × 10
= 120

Find the area by Heron's Formula.

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Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Perimeter = 540m

Ratio = 25 : 17 : 12

Now,

Assume,

Sides :-

a = 25p

b = 17p

c = 12p

Perimeter of triangle = a + b + c

540 = 25p + 17p + 12p

54p = 540

p = 540/54

p = 10

Sides of a triangle,

a = 25p = 25 × 10 = 250 m

b = 17p = 17 × 10 = 170 m

c = 12p = 12 × 10 = 120 m

Semi Perimeter,

s = (a + b + c)/2

s = (250 + 170 + 120)/2

s = 540/2

s = 270 m

Using Heron’s formula :-

A = √s(s - a)(s - b)(s - c)

A = √270(270 - 250)(270 - 170)(270 - 120)

A = √270 × (20) × (100) × (150)

A = √(9 × 3 × 10) × (2 × 10) × (10 × 10) × (10 × 15)

A = √(10 × 10 × 10 × 10) × 10 × (9) × (3) × (2) × (3 × 5)

A = √(10 × 10 × 10 × 10) × (2 × 5) × (9) × (3) × (2) × (3 × 5)

A = √(10 × 10 × 10 × 10) × (2 × 2) × (3 × 3) × (3 × 3) × (5 × 5)

A = 10 × 10 × 2 × 3 × 3 × 5

A = 100 × 90

A = 9000 m²

Therefore,

Area of triangle = 9000 m²