Question

Write the sequence of natural numbers which are multiplied by 3 and added to 1 ?​

Answer 1

Here we have,

Ratio = 3 : 4 : 5

Perimeter = 144 cm

Assume,

Sides,

a = 3x , b = 4x and c = 5x

Now,

Perimeter of Triangle = a + b + c

144 = 3x + 4x + 5x

12x = 144

x = 144/12

x = 12

Here,

Sides of triangle are :-

a = 3x = 3 × 12 = 36 m

b = 4x = 4 × 12 = 48 m

c = 5x = 5 × 12 = 60 m

Now,

Semi Perimeter of Triangle,

s = (a + b + c)/2

s = (36 + 48 + 60)/2

s = 144/2

s = 72 m

Now,

Using Heron formula :-

A = √s(s - a)(s - b)(s - c)

A = √72(72 - 36)(72 - 48)(72 - 60)

A = √72 × (36) × (24) × (12)

A = √(36 × 2) (36) (12 × 2) × 12

A = √(36 × 36 × 12 × 12) × (2 × 2)

A = 36 × 12 × 2

A = 72 × 12

A = 864 cm²

Now, here,

Longest side = 60 cm

A = ½ x Base x altitude

864 = ½ × 60 × altitude

864 = 30 × altitude

altitude = 864 / 30

altitude = 28.8 cm