If the area of a rhombus is `60cm^(2)`, then its diagonals are 10 cm and 6 cm long.

Answer

To determine whether the statement "If the area of a rhombus is 60 cm², then its diagonals are 10 cm and 6 cm long" is true or false, we can use the formula for the area of a rhombus in terms of its diagonals.

### Step 1: Understand the formula for the area of a rhombus
The area \( A \) of a rhombus can be calculated using the lengths of its diagonals \( d_1 \) and \( d_2 \) with the formula:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]

### Step 2: Substitute the given values into the formula
In this case, we are given the area \( A = 60 \, \text{cm}^2 \) and the lengths of the diagonals \( d_1 = 10 \, \text{cm} \) and \( d_2 = 6 \, \text{cm} \). We can substitute these values into the formula:
\[ 60 = \frac{1}{2} \times 10 \times 6 \]

### Step 3: Calculate the right-hand side
Now, we calculate the right-hand side:
\[ \frac{1}{2} \times 10 \times 6 = \frac{60}{2} = 30 \, \text{cm}^2 \]

### Step 4: Compare the calculated area with the given area
We find that the calculated area \( 30 \, \text{cm}^2 \) does not equal the given area \( 60 \, \text{cm}^2 \).

### Step 5: Conclusion
Since the calculated area does not match the given area, the statement is false. The diagonals of a rhombus with an area of \( 60 \, \text{cm}^2 \) cannot be \( 10 \, \text{cm} \) and \( 6 \, \text{cm} \).

---