The length of the side in Simple radical form with rational denominator=[tex]\frac{10\sqrt{3} }{3}[/tex]
Equilateral triangle:
An equilateral triangle is a triangle with all three sides of equal length, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal 60 degrees angles.
Given:
the perpendicular of the triangle = 5
Let the side of the equilateral triangle = a
Solution :
Now all the side of the triangle is is equal, so that a=x
The base of an equilateral triangle is divided into 2 equal parts, due to the perpendicular.
Now by Pythagoras equation :
[tex]p^{2} +b^{2} =h^{2}[/tex]
[tex]5^{2} +(\frac{x}{2} )^{2} =x^{2}[/tex]
[tex]25=x^{2} -\frac{x^{2} }{4}[/tex]
[tex]25 (4)=4x^{2} -x^{2} \\100=3x^{2}[/tex]
[tex]\frac{100}{3}=x^{2} \\\\\sqrt \frac{100}{3} } =x[/tex]
[tex]\frac{10}{\sqrt{3} } =x[/tex]
Simple radical form with rational denominator :
Radical form: An expression that uses a root, such as a square root, or cube root is known as a radical notation, Therefore, [tex]3^{\frac{3}{2} }[/tex] in radical form is = √27.
Convert [tex]\frac{10}{\sqrt{3} }[/tex] into radical form with rational denominator:
[tex]\frac{10}{\sqrt{3} } =\frac{10}{\sqrt{3} } .\frac{\sqrt{3} }{\sqrt{3} } \\[/tex]
[tex]\frac{10\sqrt{3} }{3}[/tex]
The length of the side in Simple radical form with rational denominator=[tex]\frac{10\sqrt{3} }{3}[/tex]
For More details: brainly.com/question/2456591
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