Question

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

Answer 1

The greatest whole possible whole number length of the unknown side is 9 inches

Solution:

Two sides of an acute triangle measure 5 inches and 8 inches

The length of the longest side is unknown

We have to find the length of unknown side

The longest side of any triangle is a hypotenuse

For a acute triangle we know:

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:

$c^2$

Here in this sum,

a = 5 inches

b = 8 inches

c = ?

Substituting we get,

$c^2< 5^2+8^2\\\\c^2 < 25 + 64\\\\c^2 < 89\\\\c < 9.4$

On rounding to nearest whole number,

c < 9

Hence, to the greatest whole possible whole number length of the unknown side is 9 inches

Answer 2

Answer:

The greatest whole possible whole number length of the unknown side is 9 inches

Step-by-step explanation: