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Hannah wants to decorate his triangular flag with a ribbon. the two sides of the flag are 8 units and 2 units. Using the triangle inequality theorem, find out how much ribbon is required for the third side

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Hannah Wants To Decorate His Triangular Flag With A Ribbon The Two Sides Of The Flag Are 8 Units And 2 Units Using The Triangle Inequality Theorem Find Out How class=

Sagot :

Fundamental Concept

Assuming that the triangular flag is a right triangle, we can refer to the pythagorean theorem which states:

[tex]a^{2} +b{2} = c^{2}[/tex]

where a, b, and c are the lengths of each side of the triangle.

Derivative Equation

From the pythagorean theorem, we can derive the formula to calculate for the length of the third side as follows:

[tex]c=\sqrt{a^{2} +b^{2} }[/tex]

Application

We can now solve for the length of the third side as follows:

[tex]c=\sqrt{8^{2} + 2^{2} }[/tex]

[tex]c = \sqrt{64 + 4}[/tex]

[tex]c = \sqrt{64}[/tex]

[tex]\sqrt{64}[/tex] can be further simplified as follows

[tex]c = \sqrt{4 x 17}[/tex]

[tex]c = 2\sqrt{17[/tex]

Considering the above, the length of the third side is [tex]2\sqrt{17}[/tex] units or 8.25 units which is also the length of ribbon required for the third side.