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Which of the following could not be the lengths of the sides of a triangle?
4 in., 6 in., 8 in.

3cm,4cm,5cm

6ft,3ft,9ft

5km,2km,4km

Which of the following could not be the lengths of the sides of a triangle? $\newline$ $4$ $in$ ., $6$ $in$ ., $8$ $in$ . $\newline$ $3 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}$ $\newline$ $6 \mathrm{ft}, 3 \mathrm{ft}, 9 \mathrm{ft}$ $\newline$ $5 \mathrm{~km}, 2 \mathrm{~km}, 4 \mathrm{~km}$

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Calculate mean, median, mode, and range

Full solution

Q. Which of the following could not be the lengths of the sides of a triangle?

\newline

4

in

.,

6

in

.,

8

in

.

\newline

3 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}

\newline

6 \mathrm{ft}, 3 \mathrm{ft}, 9 \mathrm{ft}

\newline

5 \mathrm{~km}, 2 \mathrm{~km}, 4 \mathrm{~km}

Check Triangle Inequality Theorem Set $1$ : Step $1$ : Check the triangle inequality theorem for the first set: $4\,\text{in.}$ , $6\,\text{in.}$ , $8\,\text{in.}$ $\newline$ The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. $\newline$ Calculation: $4\,\text{in.} + 6\,\text{in.} = 10\,\text{in.}$ , which is greater than $8\,\text{in.}$ ; $6\,\text{in.} + 8\,\text{in.} = 14\,\text{in.}$ , which is greater than $4\,\text{in.}$ ; $4\,\text{in.} + 8\,\text{in.} = 12\,\text{in.}$ , which is greater than $6\,\text{in.}$
Check Triangle Inequality Theorem Set $2$ : Step $2$ : Check the triangle inequality theorem for the second set: $3\,\text{cm}$ , $4\,\text{cm}$ , $5\,\text{cm}$ . Calculation: $3\,\text{cm} + 4\,\text{cm} = 7\,\text{cm}$ , which is greater than $5\,\text{cm}$ ; $4\,\text{cm} + 5\,\text{cm} = 9\,\text{cm}$ , which is greater than $3\,\text{cm}$ ; $3\,\text{cm} + 5\,\text{cm} = 8\,\text{cm}$ , which is greater than $4\,\text{cm}$ .
Check Triangle Inequality Theorem Set $3$ : Step $3$ : Check the triangle inequality theorem for the third set: $6\,\text{ft}$ , $3\,\text{ft}$ , $9\,\text{ft}$ . Calculation: $6\,\text{ft} + 3\,\text{ft} = 9\,\text{ft}$ , which is not greater than $9\,\text{ft}$ ; $3\,\text{ft} + 9\,\text{ft} = 12\,\text{ft}$ , which is greater than $6\,\text{ft}$ ; $6\,\text{ft} + 9\,\text{ft} = 15\,\text{ft}$ , which is greater than $3\,\text{ft}$ .

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