Answer:
No, it is not possible to construct a triangle that has side lengths 4 m, 5 m, and 9 m
Step-by-step explanation:
The Longest side in a Triangle is going to be the hypotenuse. For these values to construct a triangle, they would need to give us a value of 9m when plugged into the Pythagorean Theorem Formula, which is the following,
[tex]a^{2} + b^{2} = c^{2}[/tex]
in which c would be the hypotenuse. If we plug in 4m and 9m (as the hypotenuse) we can see what value side b would need to be for this triangle to be constructed.
[tex]4^{2} + b^{2} = 9^{2}[/tex]
[tex]16 + b^{2} = 81[/tex]
[tex]b^{2} = 65[/tex][tex]b = 8.062[/tex]
Seeing as how b is equal to 8.062m and not 5m we can safely say that you can NOT construct a triangle with the given side lengths.
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