In a parallelogram ABCD diagonals AC and BD intersect at O and AC = 7.4 cm and BD = 6.2 cm. Find the length of AO and BO.

Answer

To solve the problem, we need to find the lengths of AO and BO in the parallelogram ABCD, where the diagonals AC and BD intersect at point O. Given that AC = 7.4 cm and BD = 6.2 cm, we can follow these steps:

### Step 1: Understand the properties of the diagonals in a parallelogram
In a parallelogram, the diagonals bisect each other. This means that the point of intersection (O) divides each diagonal into two equal parts.

### Step 2: Set up the equations for the diagonals
Since O is the midpoint of AC, we can express the lengths as:
- AO + OC = AC
- AO = OC (since O is the midpoint)

Similarly, for diagonal BD:
- BO + OD = BD
- BO = OD (since O is the midpoint)

### Step 3: Substitute the known values into the equations
From the problem, we know:
- AC = 7.4 cm
- BD = 6.2 cm

Using the first diagonal:
- AO + OC = 7.4 cm
Since AO = OC, we can write:
- AO + AO = 7.4 cm
- 2AO = 7.4 cm

### Step 4: Solve for AO
Now, divide both sides by 2:
- AO = 7.4 cm / 2
- AO = 3.7 cm

### Step 5: Use the second diagonal to find BO
Now, using the second diagonal:
- BO + OD = 6.2 cm
Since BO = OD, we can write:
- BO + BO = 6.2 cm
- 2BO = 6.2 cm

### Step 6: Solve for BO
Now, divide both sides by 2:
- BO = 6.2 cm / 2
- BO = 3.1 cm

### Final Answer
Thus, the lengths are:
- AO = 3.7 cm
- BO = 3.1 cm