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?

Answer 1

the answer is 9

Explanation:

Answer 2

Hence, the greatest possible whole-number length of the unknown side is:

9 inches

Explanation:

A corollary to the Pythagorean Theorem states that:

If c is the longest side of a acute triangle, a and b are other two sides of a acute triangle then the condition that relates these three sides are given as:

`c^2<a^2+b^2`

Here we have:

Let a=5 inches.

b=8 inches.

Then,

`c^2<5^2+8^2\\\\c^2<25+64\\\\c^2<89\\\\c<9.434`

Hence, to the greatest whole possible whole number length of the unknown side is:

9 inches.