in square ABCD, the measure, in inches of AB is 3x+2 and BC is x+12. What is the number of inches in the length of DC ?
arent' all sides equal?
then set
3x+2 = x+12 and solve for x
sub x back into x+12 to get the length of each side
To find the length of DC, we need to use the properties of a square, which tells us that all sides are equal in length.
In this case, we are given that AB = 3x + 2 and BC = x + 12. Since AB and BC are adjacent sides of the square, they must be equal in length.
So, we can set up an equation to solve for x:
3x + 2 = x + 12
To solve for x, we can start by subtracting x from both sides of the equation:
3x + 2 - x = x + 12 - x
Simplifying the equation, we have:
2x + 2 = 12
Next, we can subtract 2 from both sides of the equation:
2x + 2 - 2 = 12 - 2
Simplifying further, we get:
2x = 10
Now, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 10/2
Simplifying again, we have:
x = 5
Therefore, the value of x is 5. To find the length of DC, we substitute this value of x back into one of the given expressions. Let's use BC = x + 12:
DC = BC = 5 + 12
DC = 17
So, the length of DC is 17 inches.