Write the negation of the following statements :
Both diagonals of a rectangle have the same length

Answer

To write the negation of the statement "Both diagonals of a rectangle have the same length," we will follow these steps:

### Step 1: Understand the Original Statement
The original statement asserts that both diagonals of a rectangle are equal in length. This is a universal statement about all rectangles.

### Step 2: Identify the Structure of the Statement
The statement can be broken down as follows:
- "Both diagonals of a rectangle" refers to the two diagonals.
- "have the same length" indicates equality.

### Step 3: Formulate the Negation
The negation of a universal statement (which asserts that something is true for all cases) is an existential statement (which asserts that there is at least one case where it is not true).

Thus, the negation of the statement can be expressed as:
- "There exists at least one rectangle whose diagonals do not have the same length."

### Step 4: Write the Negation Clearly
The final negation statement is:
- "There exists a rectangle whose diagonals do not have the same length."

### Summary of the Solution
The negation of the statement "Both diagonals of a rectangle have the same length" is:
- "There exists a rectangle whose diagonals do not have the same length."

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