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Sagot :
The equilateral triangle has a side length of 34
Here, given the altitude of an equilateral triangle, we want to get the measure of its sides
Let the sides measure be x (all sides are equal)
The altitude divides the base length into two equal parts
So, one part of the base will measure x/2
So we have a right-angled triangle with hypotenuse x , while the two other sides are x/2 and 17 root 3
Using Pythagoras' theorem, we understand that the square of the hypotenuse equals the sum of the squares of the two other sides
Mathematically, we have this as follows;
[tex]\begin{gathered} x^2\text{ = (17}\sqrt[]{3})^2\text{ + (}\frac{x}{2})^2 \\ \\ x^2\text{ = 867 + }\frac{x^2}{4} \\ \\ \text{Multiply through by 4} \\ \\ 4x^2=3468+x^2 \\ \\ 4x^2-x^2\text{ = 3468} \\ \\ 3x^2\text{ = 3468} \\ \\ x^2\text{ = }\frac{3468}{3} \\ \\ x^2\text{ = 1156} \\ \\ x^2=34^2 \\ \\ x\text{ = 34} \end{gathered}[/tex]
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