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? inches

Answer 1

As we know that the length of the third side of the triangle should be less than the sum of the lengths of the other two sides.

Now, the length of the two sides of the triangle is 5 inches and 8 inches.

So, the length of the third side should be less than the sum of lengths of other two sides:

$8+5=13$ inches.

So the greatest possible whole number length of the unknown side is 12 inches.

Answer 2

Answer:

Step-by-step explanation:

Concept :

• An elementary polygon having three sides and three vertices is a triangle.
• There are three interior angles because it has three sides.
• An acute angle is one that ranges in measurement from $0^{\circ}$ to $90^{\circ}$. A form of triangle called an acute triangle has acute angles at each of its three internal angles. Triangles with sharp angles are also known as acute triangles.
• Acute triangles have different side lengths, but their interior angles are always less than $90^{\circ}$.

Given:

Two sides of acute triangle $5$ $inches$ and $8$  $inches$

Find:

Longest Possible length of third side

Solution :

• Let the triangle be $XYZ$.  By triangle inequality, the sum of length of any two sides( $XY$ or $YZ$ or $XZ$)   must be greater than the length of the third side.  Assume , the third side be $XZ$.

      i.e. $(XY + YZ ) > XZ$

• From given data , assume  $XY = 5$ $inches$  and $YZ = 8$ $inches$

                             $XZ < (XY + YZ)\\\\XZ < ( 5 + 8)\\\\XZ < 13$

Hence , the longest possible length must be less than $13$  $inches$  which is $12$ $inches$

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