Question

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

Answer 1

9 inches

Explanation:

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

Answer 2

Answer: 9 inches

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.