QUADRILATERAL ABCD IS A RECTRANGLE
IF AC=2X+13 AND DB=4X-1 FIND DB
in a rectangle the diagonals are equal.
2x+13 = 4x-1
2x = 14
x=7
AC = DB = 27
27
If AC = x + 3 and DB = 3x – 19, find AC.
To find the length of DB in the given rectangle ABCD, we can use the information provided about the lengths of AC and DB.
Given: AC = 2x + 13 and DB = 4x - 1
Since ABCD is a rectangle, opposite sides are equal in length. Therefore, we know that AC is equal to BD.
So, we can equate AC and DB:
2x + 13 = 4x - 1
To isolate the variable x, we can first simplify the equation by subtracting 2x from both sides:
13 = 2x - 1
Next, we can add 1 to both sides to get rid of the -1:
13 + 1 = 2x - 1 + 1
14 = 2x
Finally, divide both sides by 2 to solve for x:
14/2 = 2x/2
7 = x
Now that we know the value of x, we can substitute it back into the equation for DB:
DB = 4x - 1
DB = 4(7) - 1
DB = 28 - 1
DB = 27
Therefore, the length of DB is 27 units.