Scalene triangle

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Definition of Scalene Triangle

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

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

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Next, we will see some examples of scalene triangles:


Examples and Exercises with Solutions for Scalene Triangle

examples.example_title

Given an equilateral triangle:

XXX

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

examples.explanation_title

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 x+x+x=33

3x=33 3x=33

We divide the two sections by 3:

3x3=333 \frac{3x}{3}=\frac{33}{3}

x=11 x=11

examples.solution_title

11

examples.example_title

AAABBBCCCDDD

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!)

examples.explanation_title

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 AB=BC=CD=DA

But the diagonal AC is not equal to them.

Therefore, the two previous triangles are isosceles:

AD=DC AD=DC

AB=BC AB=BC

examples.solution_title

Right triangles

examples.example_title

Given the isosceles triangle ABC,

The side AD is the height in the triangle ABC

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and inside it, EF is drawn:

AF=5 AB=17
AG=3 AD=8

What is the perimeter of the trapezoid EFBC?

examples.explanation_title

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: A2+B2=C2 A^2+B^2=C^2 in the triangle AFG

We replace

32+GF2=52 3^2+GF^2=5^2

We isolate GF and solve:

9+GF2=25 9+GF^2=25

GF2=259=16 GF^2=25-9=16

GF=4 GF=4

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

82+DB2=172 8^2+DB^2=17^2

64+DB2=289 64+DB^2=289

DB2=28964=225 DB^2=289-64=225

DB=15 DB=15

We start by finding FB:

FB=ABAF=175=12 FB=AB-AF=17-5=12

Now we reveal EF and CB:

GF=GE=4 GF=GE=4

DB=DC=15 DB=DC=15

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

EF=GF×2=4×2=8 EF=GF\times2=4\times2=8

CB=DB×2=15×2=30 CB=DB\times2=15\times2=30

All that's left is to calculate:

30+8+12×2=30+8+24=62 30+8+12\times2=30+8+24=62

examples.solution_title

62

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