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Two sides of an acute triangle measure 5 inches and 8 inches. The longest side is unknown.


What is the greatest possible whole-number length of the unknown side?


_____ in

Verified Answer :

Answer:   9 inches

Step-by-step explanation:

Let x be the longest side of the acute triangle having other sides 5 inches and 8 inches,

Since, for the acute triangle,

\((\text{longest side})^2< \text{ sum of the square of the other sides}\)

\(\implies x^2 < 5^2 + 8^2\)

\(\implies x^2< 25 + 64\)

\(\implies x^2 < 89\)

\(\implies x < 9.43398113\approx 9.434\)

Thus, the largest value of x ( whole number ) is 9.

gbprulesmile

Answer:

9 inches

Step-by-step explanation:

I answered this before and it was deleted. So here it is again.

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