What can you tell about a triangle when given three side lengths?

Mathematics

1 answer:

Whitepunk [10]3 years ago

4 0

Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.

Step-by-step explanation:

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%3F%7D%7B5%7D%20%2A%20%5Cfrac%7B10%7D%7B8%7D%20%3D1.5%5C%5C" id="TexFormula1" title=

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$\boxed{\sf \huge \boxed{ \sf ?} = 6}$

Step-by-step explanation:

$\sf Solve \: for \: \boxed{ \sf ?} : \\ \sf \implies \frac{\boxed{ \sf ?}}{5} \times \frac{10}{8} = 1.5 \\ \\ \sf \implies \frac{\boxed{ \sf ?} \times 10}{5 \times 8} = 1.5 \\ \\ \sf \frac{10}{5} = \frac{ \cancel{5} \times 2}{ \cancel{5}} = 2 : \\ \sf \implies \frac{ \boxed{ \sf 2} \times \boxed{ \sf ?} }{8} = 1.5 \\ \\ \sf \frac{2}{8} = \frac{ \cancel{2}}{ \cancel{2} \times 4} = \frac{1}{4} : \\ \sf \implies \frac{\boxed{ \sf ?}}{ \boxed{ \sf 4}} = 1.5 \\ \\ \sf Multiply \: both \: sides \: of \: \frac{\boxed{ \sf ?}}{4} = 1.5 \: by \: 4 : \\ \sf \implies \frac{4 \times \boxed{ \sf ?}}{4} = 4 \times 1.5 \\ \\ \sf \frac{4 \times \boxed{ \sf ?}}{4} = \frac{ \cancel{4}}{ \cancel{4}} \times \boxed{ \sf ?} = \boxed{ \sf ?} : \\ \sf \implies \boxed{\boxed{ \sf ?}} = 4 \times 1.5 \\ \\ \sf 4 \times 1.5 = 6 : \\ \sf \implies \boxed{ \sf ?} = 6$

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