Can a triangle have the following side lengths? Explain. 5 feet, 2 feet, 10 feet

Mathematics

1 answer:

leva [86]3 years ago

3 0

Answer:

No, this can not be a triangle because if you use the Pythagorean theorem 5 squared plus 2 squared doesn't equal 10 squared.

Step-by-step explanation:

You take 5 squared and 2 squared and add them, you then find the square root and that should equal 10, if not its not a triangle.

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Answer: $\bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}$

<u>Step-by-step explanation:</u>

Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square. Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

$90^2+90^2=c^2\\8100+8100=c^2\\16200=c^2\\\sqrt{16200}=c\\\boxed{90\sqrt2}=c\qquad \qquad \text{which is approximately 127.28}\\\\\\\\\text{Halfway between home plate and 2nd base means divide that length by 2:}\\\\\dfrac{90\sqrt2}{2}=\boxed{45\sqrt2}$