The sides or edges of a triangle

Recall that the perimeter of a plane figure is its edge, so in a triangle the perimeter is the sum of its three sides (edges).

In any triangle the sum of the length of any two of its sides must be greater than the length of the third side.

Given a triangle with sides $4~cm$, $3~cm$ and $5~cm$. Calculate the perimeter.

Solution

We know that the perimeter of a triangle is the sum of its three sides, therefore,

$P=4\operatorname{cm}+3\operatorname{cm}+5\operatorname{cm}$

Answer:

$P=12\operatorname{cm}$

Tell if it is possible to construct a triangle in which its sides measure $3~cm$, $4~cm$ and $8~cm$.

Solution

Recall that in order to construct a triangle, the sum of any two sides must be greater than the third side.

If we add the sides with measures $3~cm$ and $4~cm$, we get as a result $7~cm$, which is less than the third side.

Answer:

Therefore, it is not possible to construct a triangle with the given measures.

If an equilateral triangle has perimeter $P=21\operatorname{cm}$. How long is each side?

Solution

Since the triangle is equilateral we know that its sides are equal, so we just divide the perimeter by three to get the measure of each side. lado.

$P=3x$

$21\operatorname{cm}=3x$

$x=21\operatorname{cm}:3$

Answer:

$x=7\operatorname{cm}$

Tell if it is possible to construct a triangle in which its sides measure $5~cm$, $7~cm$ and $10~cm$.

Solution

We add the lengths of any two sides (edges) and compare with the length of the remaining side.

• $5~cm + 7~cm= 12~cm$which is greater than the remaining side that measures $10~cm$
• $7~cm + 10~cm = 17~cm$The length of the remaining side, which is greater than the remaining side measuring $5~cm$, is greater than the remaining side measuring $5~cm$.
• $10~cm + 5~cm = 15~cm$, which is greater than the remaining side measuring $7~cm$.

Answer:

So if it is possible to construct a triangle of measures $5~cm$, $7~cm$ and $10~cm$ on each side.

How many sides does a triangle have?

A triangle has three sides.

How many edges does a triangle have?

A triangle has three edges.

What are the edges of a triangle?

The edges of a triangle, commonly called the sides of a triangle, are the straight lines that bound the faces of the triangle.

What are the edges of a figure?

In a plane figure, the edges or sides are the line segments that join two vertices, and form the outline or perimeter of the figure.

Query

$DE$ Does that side not exist as part of any of the triangles?

Solution

A side in a triangle is a line that passes between one of the 3 points that are the angles of the triangle.

In this case the line $DE$ does not pass between the extreme angles of any of the triangles but goes out through a point $D$ which is in fact an angle in a triangle $\triangle DBC$ but $DE$ ends at the point $E$ which is not an angle in any of the triangles in the figure.

Answer

True

Question:

Do the triangles in the drawing overlap?

Solution

We can observe that according to the theorem of superposition: side, side, angle.

We can observe that there are 2 sides equal in length and an angle equal in size.

Answer

Yes

Question

What type of triangle is drawn here?

Solution

It can be seen that in this triangle each of its three angles is of different size so it can be said that it is a scalene triangle.

Answer

Scalene triangle

Consigna

Given the following triangle:

The perimeter of the triangle is $17$

How much is $X$?

Solution

To solve the task we replace all the data we have in the equation to calculate the perimeter of the triangle:

$2X+3X+3.5X=17$

Let's remember... The perimeter of the triangle is equal to the sum of its 3 sides.

If we calculate the equation we find that:

$8.5X=17$

We divide the equation by $8.5$ to find the value of. $X$

$\frac{8.5X}{8.5}=X=\frac{17}{8.5}=2$

Answer

$2$

Request

Given the equilateral triangle

The perimeter of the triangle is $33\operatorname{cm}$, what is the value of $X$?

Solution

One of the characteristics of an equilateral triangle is obviously that each of its sides are equal, i.e. if one side is worth $11$ all its sides will be equal to $11$

Answer

$11$