Final answer:
The value of x in the rhombus ABCD with sides 5x+25 and 7x-1 is 13.
Step-by-step explanation:
To find the value of x in the rhombus ABCD with sides 5x+25 and 7x-1, we can use the fact that opposite sides of a rhombus are equal in length.
So, we can set the two expressions for the sides equal to each other: 5x+25 = 7x-1.
Next, we can solve this equation for x. Subtracting 5x from both sides gives 25 = 2x-1, and adding 1 to both sides gives 26 = 2x. Dividing both sides by 2 gives x = 13.