等边三角形的周长和边长有什么关系？

等边三角形是一个二维图形，其中所有的角和边完全相等。它也被称为等角三角形，因为它的所有角度都等于 60°。它是由三个相等的边组成的正多边形。

等边三角形的性质

• 三边相等。
• 所有三个角度都相等，即各 60°。
• 在等边三角形中，中线、角平分线和高度都相等。
• 面积由 √3/4(a)square 给出。
• 所有的角度都相互一致。

周长

等边三角形的周长由该图所有边的总和给出。由于等边三角形由三个相等的边组成，因此周长由所有这些边的总和给出。

让我们假设等边三角形的边是a。

现在，周长 P 由下式给出，

P = a + a + a

P = 3a

因此，等边三角形的周长等于三角形边长的三倍。

示例问题

问题1.如果等边三角形的边是2√3。然后求等边三角形的周长？

解决方案：

Here we have to find the perimeter of the equilateral triangle

We are given that the side of an equilateral triangle is 2√3

As we know that

Perimeter of an equilateral triangle = Side + Side + Side

Perimeter of an equilateral triangle = 2√3 + 2√3 +2√3

Perimeter of an equilateral triangle = (2 + 2 + 2)√3

Perimeter of an equilateral triangle = 6√3

问题2.假设等边三角形公园的周长是543m，那么找到等边三角形公园的边？

解决方案：

Here we have to find the sides of the equilateral triangular park using its perimeter

Given,

The perimeter of equilateral triangular park = 543 m 

As we know that

Perimeter of equilateral triangular park = Side + Side + Side = a + a + a = 3a

Perimeter of equilateral triangular park = 543 m = 3a

543 = 3a

a = $\frac{543}{3}$

a = 181 m

Therefore,

Side of the equilateral triangular park is 181 m.

问题 3。如果三角形学校操场的所有边都相等，即 50 m，则计算三角形学校操场的围栏成本。如果每米围栏的成本是23 卢比。

解决方案：

Here we have to find the cost of fencing of triangular school playground

For that first, we have to find the perimeter of the playground

As we know that

Perimeter of triangle = side + side + side

Therefore,

Perimeter of triangular school playground = 50 + 50 + 50

Perimeter of triangular school playground = 150 m

Now we will find the cost of fencing the playground

According to the question

Cost of fencing per meter is ₹23

Therefore,

Cost of fencing 150 m = 23 × 150 = ₹3450

Hence,

The cost of fencing the school playground is ₹3450.

问题 4. 等边三角形招牌围板的周长为 450 厘米。找到标牌囤积的区域？

解决方案：

Here we have to find the area of the triangular sign hoarding

For that first, we need to find the side of the equilateral triangular sign hoarding

According to the question

The perimeter of the triangular sign hoarding = 450 cm

As we know that

Perimeter of the triangular sign hoarding = Side + Side + Side = 3a

3a = 450

a = $\frac{450}{3}$

a = 150 cm

Further finding the area of sign board

Area of equilateral triangle = $\frac{\sqrt3}{4}a^2$

Area of equilateral triangle = $\frac{\sqrt3}{4}\times 150^2$

Area of equilateral triangle = 5625√3

问题 5. 如果等边三角形的边是 20√5。然后求等边三角形的周长？

解决方案：

Here we have to find the perimeter of the equilateral triangle

We are given that the side of an equilateral triangle is 20√5

As we know that

Perimeter of an equilateral triangle = Side + Side + Side

Perimeter of an equilateral triangle = 20√5 + 20√5 +20√5

Perimeter of an equilateral triangle = (20 + 20 + 20)√5

Perimeter of an equilateral triangle = 60√5