The lengths of the sides of a quadrilateral are 2011 cm, 2012 cm, 2013 cm and x cm. If x is an integer, what is the largest possible value of x?
Help is badly needed. my teacher frightens me huhu. please
Think of laying out the 3 given sides in a straight line
to get a sum of 2011+2012+2013 = 2036
As long as x is < 2036 you will be able to "kink" the 3 lines at their joints and form a quad.
If x = 2036, they will all lie on a straight line.
if x > 2036, you can't join the end of that long side to the end of the others
so x < 2036
To find the largest possible value of x in the given quadrilateral, we can use the triangle inequality theorem.
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. For a quadrilateral, the sum of any two sides must be greater than the sum of the other two sides.
Let's apply this theorem to the given quadrilateral:
2011 cm + 2012 cm > 2013 cm
4023 cm > 2013 cm
2011 cm + 2013 cm > 2012 cm
4024 cm > 2012 cm
2012 cm + 2013 cm > 2011 cm
4025 cm > 2011 cm
Now, let's find the largest possible value of x. Since the sum of any two sides must be greater than the sum of the other two sides, we can conclude that:
x + 2013 cm > 4025 cm
x > 2012 cm
Therefore, the largest possible value of x is 2012 cm.
To find the largest possible value of x, we need to understand the properties of a quadrilateral.
In any quadrilateral, the sum of the lengths of any three sides must be greater than the length of the fourth side. This is known as the Triangle Inequality Theorem.
So, in this case, we can write down the inequality:
2011 cm + 2012 cm + 2013 cm > x cm
Now, let's simplify and solve for x:
6036 cm > x cm
Since x needs to be an integer, the largest possible value of x is the largest integer that is less than 6036 cm.
We can use the floor function (or integer division) to find this value. By dividing 6036 cm by 1, we get the largest possible integer value for x:
x = floor(6036 cm / 1) = 6036 cm
Therefore, the largest possible value of x is 6036 cm.