Nathan wants to draw a triangle. He knows that two of the side lengths are 4 inches and 8 inches. What would be the smallest whole number for the third side?

5

Step-by-step explanation:

Hi, the sum of the lengths of the 2 sides given is equal to =8 +4 =12

And the difference of the lengths of 2 sides given is = 8-4=4

So, for any triangle the length of a side  must less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

When can write this as an inequality :

4<X <12

Where x is the value of the third side.

According to the inequality, the smallest value for the third side would be 5 ( because it must be greater than 4 , not greater or equal)

The third side would measure 7 inches (approximately)

Step-by-step Explanation: In any given triangle the size of the angles are as important as the length of the sides. That would determine which formula to apply in solving for any unknown side or angle. In a triangle with two sides given, like we have here the size of one or two of the angles would help in the calculation of the third side. But where no angle is provided, we shall assume it is a right angled triangle. It cannot be an equilateral triangle (because ALL SIDES must be equal), and we cannot tell if it’s an isosceles triangle (because TWO ANGLES MUST be equal) since no angle was given.

Therefore following our assumption, we can use the Pythagoras theorem which states that;

AC^2 = AB^2 + BC^2

Where AC is the longest side (hypotenuse) and AB and BC are the other two sides. The question requires us to calculate the smallest whole number, and hence we shall take the side measuring 8 as the hypotenuse. We can now substitute for the known values,

8^2= AB^2 + 4^2

64 = AB^2 + 16

AB^2 = 64 - 16

AB^2 = 48

Add the square root sign to both sides of the equation

AB = 6.9282

Rounded to the nearest whole number, the third side would measure 7 inches.