Question

12.
A triangle of area 9y cm2? has been drawn such that its area is equal to area of equilateral
triangle of sides 6 cm then y is
* √2 cm
*√3 cm
*2cm
*3 cm​

Answer 1

Answer :

The value of y is √3 cm. [ Option 2 ]

Step-by-step explanation :

Given :

• Area of triangle = 9y cm²

• Side of the triangle = 6 cm.

To find :

• Value of y = ?

SoluTion :

We'll solve the question by using Area of a equilateral triangle.

Area of equilateral triangle is given by,

➝ A = √3/4 × a²

➝ A = √3/4 × 6²⠀⠀⠀⠀eqn(1).

Now, as the area of the triangle is given,

So,

➟ A = 9y

➟ √3/4 × 6² = 9y [From eqn(1).]

➟ √3/4× 36 = 9y

➟ √3 × 9 = 9y

➟ y = √3 × 9 / 9

➟ y = √3 cm.

Hence, the value of y is √3 cm .

Some important formulae :

1. Area of equilateral triangle = √3/4 × a²

2. Area of isosceles triangle = b×h/2

3. Area of scalene triangle = 1/2 × b × h

4. Area of triangle(Herons formula) :

⠀A = √s(s -a) (s -b) (s - c)

Answer 2

Answer:

Given :-

The area of an equilateral triangle with side 6 cm

To find :-

Area of equilateral triangle

Solution :-

Side of equilateral triangle = 6 cm

As we know that

→ Area of equilateral triangle

→ √3/4 × a²

where " a " is side of equilateral triangle

According to the question

a = 6

→ √3/4 × a²

Put the value of " a "

→ √3/4 × (6)²

→ √3/4 × 6 × 6

→ √3/2 × 3 × 6

→ √3 × 3 × 3

→ 9√3 cm²

Hence,

Area of equilateral triangle is 9√3cm²

Therefore, the correct option is 9√3cm²

More to know :-

Area of circle = πr²

Circumference of circle = 2πr

Perimeter of rectangle =2(l + b)

Perimeter of square = 4 × side

Area of square = side × side

Area of rhombus = ½ × product of diagonals

Area of Parallelogram = base × height

Area of trapezium = ½ × sum of parallel sides × height