one side of a triangle is 4 cm. The sum of the two other sides is 11 and all sides are integers. What is the largest possible side.
the longest side must be less than the sum of the two shorter side
the difference between the longest and shortest sides must be less than the middle side
L + A = 11
L < (A + 4) ... L < (11 - L + 4)
... 2 L < 15 ... L < 7.5
L = 7, A = 4
To find the largest possible side of the triangle, we need to consider the remaining sides when one side is already given as 4 cm and the sum of the other two sides is 11.
Let's assume the other two sides of the triangle as 'a' and 'b', where a and b are integers.
According to the problem statement, we have the following equation:
a + b = 11 - 4
a + b = 7
To find the largest possible side, we need to find the maximum value for either 'a' or 'b'.
Since both 'a' and 'b' are integers, the maximum possible value for either 'a' or 'b' in this case will be (7 - 1) = 6. This means one side could be 6 cm and the other side could be 1 cm.
Therefore, the largest possible side of the triangle is 6 cm.
To find the largest possible side of the triangle, we need to consider the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
In this case, one side of the triangle is given as 4 cm. Let's call the other two sides x and y (where x ≥ y). According to the problem, the sum of the other two sides is 11 cm: x + y = 11.
To find the largest possible side, we can start by considering the maximum value for x. Since the sum of the other two sides must be greater than the remaining side, the largest possible value for x will be one less than the sum of the other two sides: x = 11 - 1 = 10.
Now that we have the maximum value for x, let's substitute it back into the equation x + y = 11 to solve for y:
10 + y = 11
y = 11 - 10
y = 1
So, the largest possible side of the triangle is 10 cm.