what is the length of CE if DC=5x-24, CE= 6x-20, and DE= 55?
I will assume that D , C , and E are points on a straight line, with C between D and E. Then ...
5x-24 + 6x-20= 55
11x= 99
x = 9
then CE = 6(9)-20
= 34
To find the length of CE, let's first understand the given information. We have DC = 5x - 24 and DE = 55. We need to find CE, which is given as 6x - 20.
Next, we can use the properties of a triangle to find the length of CE. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have DE = 55, DC = 5x - 24, and CE = 6x - 20. So, we can write the following inequalities:
DE + DC > CE
DC + CE > DE
CE + DE > DC
Substituting the given values, we get:
55 + (5x - 24) > (6x - 20)
(5x - 24) + (6x - 20) > 55
(6x - 20) + 55 > (5x - 24)
Now, let's solve these inequalities to find the value of x and the corresponding length of CE.
55 + 5x - 24 > 6x - 20
31 + 5x > 6x - 20
20 + 6x > 5x - 24
Rearranging these equations, we get:
5x - 6x > -20 - 31
6x - 5x > 20 + 24
Simplifying further, we have:
-x > -51
x > -7
x > 44
Since we want to find the length of CE, we can substitute the value of x back into the equation CE = 6x - 20.
CE = 6(44) - 20
CE = 264 - 20
CE = 244
Therefore, the length of CE is 244 units.