Question

the perimeters of a rectangle and an equilateral triangle are equal. what is the equation for this scenario?rectangle’s perimeter:equilateral triangle’s perimeter:scenario’s equation:

Answer 1

Answer:

The equation for scenario is 2(l + b) = 3a

The rectangle’s perimeter is 2(l + b)

The equilateral triangle’s perimeter is 3a

What is perimeter ?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

According to question

The perimeters of a rectangle and an equilateral triangle are equal.

So

let,

The length and breadth of the rectangle are l & b

And

Side of an equilateral triangle is a

Now

The rectangle’s perimeter = 2(length + breadth)

⇒ 2(l + b)

And

The equilateral triangle’s perimeter = Sum of All sides

⇒ a + a + a

⇒ 3a

Therefore

    perimeters of a rectangle = perimeters an equilateral triangle

              2(l + b) = 3a

hence, 2(l + b) = 3a is the equation which show that perimeter of rectangle and equilateral triangle is equal.

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Answer 2

The total length of a boundary defines the perimeter of an equilateral triangle.

What is the Perimeter of an Equilateral Triangle?

• The total of the three sides makes up the perimeter of an equilateral triangle.
• The following fundamental characteristics define a triangle as being equilateral:

1. The three sides are equal.
2. There is a 60° angle between all three.

• The sides of the triangle PQ = QR = RP in the following illustration have equal lengths.
• The triangle's angles are also equal in addition to this. An equilateral triangle is what this is.
• An equilateral triangle's perimeter is now equal to 3a, where a denotes one of the triangle's sides.

• Perimeter of Equilateral Triangle Formula : P = 3a, where 'a' stands for one of the triangle's sides, is a simple formula for calculating an equilateral triangle's perimeter. An equilateral triangle has three equal sides, hence the sum is equal to three equal sides, or 3a.

• Additional equilateral triangle formulas include the following: When we need to determine a triangle's height from its sides, we can apply the following formula: Equilateral Triangle Height = (3a)/2

• The semi-perimeter of an equilateral triangle must be determined in a few situations. Half of a perimeter, or semi-perimeter, is equal to 3a/2, which is derived using the formula semi-perimeter = (a + a + a)/2.

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