Question

The perimeter of an equilateral triangle is 60 m . its area is
10√3 m^2 (b) 100√3 m^2 (c) 15√3 m^2 (d) 20√3m^2​

Answer 1

Answer:

Option (b)

Step-by-step explanation:

Given :-

The perimeter of an equilateral triangle is 60 m .

To find :-

Find its area ?

Solution :-

Given that

The perimeter of an equilateral triangle is 60 m .

We know that

The perimeter of an equilateral triangle whose side a units is 3a units

=> 3a = 60

=> a = 60/3

=> a = 20 m

The side of the equilateral triangle = 20 m

We know that

Area of an equilateral triangle is (√3/4)a² sq.units

On Substituting the value of a in the above formula then

=> Area = (√3/4)×(20)² m²

=> Area = (√3/4)×(20×20) m²

=> Area = (√3/4)×(400) m²

=> Area = (√3×400)/4 m²

=> Area = √3 × 100 m²

=> Area = 100 √3 m²

Answer:-

Area of the given equilateral triangle for the given problem is 100√3 m²

Used formulae:-

Perimeter of an equilateral triangle:-

• The perimeter of an equilateral triangle whose side a units is 3a units

Area of an equilateral triangle:-

• Area of an equilateral triangle is (√3/4)a² sq.units

Answer 2

Answer :

• Area is 100√3 m²
• Option (b)

Given :

• The perimeter of an equilateral triangle is 60m

To find :

• Area

Solution :

Here , all sides are equal so,

• Let the sides be x

➞ x + x + x = 60

➞ 3x = 60

➞ x = 60/3

➞ x = 20m

Sides = 20m

Finding the semi Perimeter of triangle

We know that

• Semi perimeter = a + b + c/2

➞ Semi perimeter = 20 + 20 + 20 / 2

➞ Semi perimeter = 60/2

➞ Semi perimeter = 30m

Finding the area :

We know that,

• A = √s(s - a) (s - b) (s - c)

where ,

• A is area
• S is semi perimeter of triangle
• a , b , c is sides

➞ √s(s - a) (s - b) (s - c)

➞ √30(30 - 20) (30 - 20) (30 - 20)

➞ √30 × 10 × 10 × 10

➞ √3 × 10 × 10 × 10 × 10

➞ 10 × 10 √3

➞ 100√3

➞ 100√3 m²

Hence , Area is 100√3 m²