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

Question

asked Apr 17, 2017 218k views

2 Answers

Zsolt Szilagyi · Answer 1 · 2017-04-22T01:00:08+0000

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.