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SESSMENT
estion Id : 1510241
In each case, determine if the sides form a right triangle. If they do, place in the Yes column. If they do not, place in the No column.
Yes
No

9,12,14

6,9,12

5,12,13

3,4,5

SESSMENT $\newline$ estion Id : $1510241$ $\newline$ In each case, determine if the sides form a right triangle. If they do, place in the Yes column. If they do not, place in the No column. $\newline$ Yes $\newline$ No $\newline$ $9,12,14$ $\newline$ $6,9,12$ $\newline$ $5,12,13$ $\newline$ $3,4,5$

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Triangle Inequality Theorem

Full solution

Q. SESSMENT

\newline

estion Id :

1510241

\newline

In each case, determine if the sides form a right triangle. If they do, place in the Yes column. If they do not, place in the No column.

\newline

Yes

\newline

No

\newline

9,12,14

\newline

6,9,12

\newline

5,12,13

\newline

3,4,5

Check Triangle Sides: To check if the sides form a right triangle, use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $c$ is the longest side. For the set $9$ , $12$ , $14$ , assume $14$ is the hypotenuse. Calculate $9^2 + 12^2$ and compare it to $14^2$ . $\newline$ Calculation: $9^2 + 12^2 = 81 + 144 = 225$ , $14^2 = 196$ . $\newline$ Since $225 \neq 196$ , these sides do not form a right triangle.
Calculate for $9$ , $12$ , $14$ : For the set $6$ , $9$ , $12$ , assume $12$ is the hypotenuse. Calculate $6^2 + 9^2$ and compare it to $12^2$ . $\newline$ Calculation: $6^2 + 9^2 = 36 + 81 = 117$ , $12^2 = 144$ . $\newline$ Since $117 \neq 144$ , these sides do not form a right triangle.
Calculate for $6$ , $9$ , $12$ : For the set $5$ , $12$ , $13$ , assume $13$ is the hypotenuse. Calculate $5^2 + 12^2$ and compare it to $13^2$ . $\newline$ Calculation: $5^2 + 12^2 = 25 + 144 = 169$ , $13^2 = 169$ . $\newline$ Since $169 = 169$ , these sides form a right triangle.
Calculate for $5$ , $12$ , $13$ : For the set $3$ , $4$ , $5$ , assume $5$ is the hypotenuse. Calculate $3^2 + 4^2$ and compare it to $5^2$ . $\newline$ Calculation: $3^2 + 4^2 = 9 + 16 = 25$ , $5^2 = 25$ . $\newline$ Since $25 = 25$ , these sides form a right triangle.

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