The sides of a triangle are in the ratio 5: 12 : 13, and its perimeter

1.	The sides of a triangle are in the ratio 5: 12 : 13, and its perimeter is 150 m. Find the area of the triangle.
Answer» Perimeter of triangle = 150 m (given) Let the sides of triangle be, a, b and c, On dividing 150 m in the ratio 5 : 12 : 13, we get a = 5x cm b = 12x cm c = 13x cm We know that, Perimeter of a triangle = Sum of all the sides = a + b + c 150 = 5x + 12x + 13x = 30 x x = 5 Sides are: a = 5x = 25 cm b = 12x = 60 cm c = 13x = 65 cm Now, Let a, b and c be the sides of a triangle. Apply Heron's Formula to find the area of triangle. Area = \(\sqrt{S(S-a)(S-b)(S-c)}\) Where S = \(\frac{a + b + c}{2}\) S = 1/2(25+60+65) = 75 cm Area = √(75(75-25)(75-60)(75-65)) = √(75 × 50 × 15 × 10) = 750 Area of triangle is 750 cm².

The sides of a triangle are in the ratio 5: 12 : 13, and its perimeter is 150 m. Find the area of the triangle.

Answer»

Perimeter of triangle = 150 m (given)

Let the sides of triangle be, a, b and c,

On dividing 150 m in the ratio 5 : 12 : 13, we get

a = 5x cm

b = 12x cm

c = 13x cm

We know that, Perimeter of a triangle = Sum of all the sides = a + b + c

150 = 5x + 12x + 13x

= 30 x

x = 5

Sides are:

a = 5x = 25 cm

b = 12x = 60 cm

c = 13x = 65 cm

Now,

Let a, b and c be the sides of a triangle.

Apply Heron's Formula to find the area of triangle.

Area = \(\sqrt{S(S-a)(S-b)(S-c)}\)

Where S = \(\frac{a + b + c}{2}\)

S = 1/2(25+60+65) = 75 cm

Area = √(75(75-25)(75-60)(75-65))

= √(75 × 50 × 15 × 10)

= 750

Area of triangle is 750 cm².