**An scalene triangle is a triangle that has all its sides of different lengths.**

**An scalene triangle is a triangle that has all its sides of different lengths.**

Calculate the size of angle X given that the triangle is equilateral.

**Next, we will see some examples of scalene triangles:**

Given an equilateral triangle:

The perimeter of the triangle is 33 cm, what is the value of X?

We know that in an equilateral triangle all sides are equal,

Therefore, if we know that one side is equal to X, all sides are equal to X.

We know that the perimeter of the triangle is 33.

The perimeter of the triangle is equal to the sum of the sides together.

We replace the data:

$x+x+x=33$

$3x=33$

We divide the two sections by 3:

$\frac{3x}{3}=\frac{33}{3}$

$x=11$

11

ABCD is a square, and a diagonal AC is drawn there.

How can we define the triangles ABC and ACD?

(Attention! There may be more than one correct answer!)

Since ABCD is a square, all its angles measure 90 degrees.

Therefore, angles D and B are equal to 90°, that is, they are right angles,

Therefore, the two triangles ABC and ADC are right triangles.

In a square all sides are equal, therefore:

$AB=BC=CD=DA$

But the diagonal AC is not equal to them.

Therefore, the two previous triangles are isosceles:

$AD=DC$

$AB=BC$

Right triangles

Given the isosceles triangle ABC,

The side AD is the height in the triangle ABC

and inside it, EF is drawn:

AF=5 AB=17

AG=3 AD=8

What is the perimeter of the trapezoid EFBC?

To find the perimeter of the trapezoid, all its sides must be added:

We will focus on finding the bases.

To find GF we use the Pythagorean theorem: $A^2+B^2=C^2$in the triangle AFG

We replace

$3^2+GF^2=5^2$

We isolate GF and solve:

$9+GF^2=25$

$GF^2=25-9=16$

$GF=4$

We perform the same process with the side DB of the triangle ABD:

$8^2+DB^2=17^2$

$64+DB^2=289$

$DB^2=289-64=225$

$DB=15$

We start by finding FB:

$FB=AB-AF=17-5=12$

Now we reveal EF and CB:

$GF=GE=4$

$DB=DC=15$

This is because in an isosceles triangle, the height divides the base into two equal parts so:

$EF=GF\times2=4\times2=8$

$CB=DB\times2=15\times2=30$

All that's left is to calculate:

$30+8+12\times2=30+8+24=62$

62

Test your knowledge

Question 1

Is the triangle in the drawing an acute-angled triangle?

Question 2

Is the triangle in the drawing an acute-angled triangle?

Question 3

Is the triangle in the drawing an acute-angled triangle?

Related Subjects

- Area
- Area of Equilateral Triangles
- Area of a Scalene Triangle
- Area of Isosceles Triangles
- Area of a right triangle
- Trapezoids
- Parallelogram
- Perimeter of a Parallelogram
- Kite
- Area of a Deltoid (Kite)
- The Area of a Rhombus
- Congruent Triangles
- How is the radius calculated using its circumference?
- The Center of a Circle
- Area of a circle
- Congruent Rectangles
- Triangle similarity criteria
- Triangle Height
- Midsegment
- Exterior angle of a triangle
- Relationships Between Angles and Sides of the Triangle
- Relations Between Sides of a Triangle
- Rhombus, kite, or diamond?
- Perimeter
- Triangle
- Angles In Parallel Lines