Connect with knowledgeable individuals and get your questions answered on IDNLearn.com. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.
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]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.
