To find the length of each diagonal of the rectangle, let's follow these steps:
1. **Find the Length and Width of the Rectangle**:
Let the two sides of the rectangle be 3x and 4x (since the ratio is 3:4). The perimeter of a rectangle is given by the formula: \( 2(length + width) \). Given that the perimeter is 98 cm, we can write this as:
\( 2(3x + 4x) = 98 \)
Simplify this equation to find the value of x.
2. **Calculate the Length and Width**:
Once you find the value of x, you can determine the length and width of the rectangle. Length = 3x and Width = 4x.
3. **Use Pythagorean Theorem to Find Diagonals**:
The diagonals of a rectangle can be found using the Pythagorean theorem. The formula for the diagonal of a rectangle is \( \sqrt{(length^2 + width^2)} \).
Substitute the values of length and width into the formula to calculate the length of each diagonal.
By following these steps, you can find the length of each diagonal of the rectangle given the ratio of sides and the perimeter.
