A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measures 120 m and 44 m. If one of the sides of the parallelogram measures 66 m, find its corresponding altitude.

Options

A. `40` m
B. `50` m
C. `60` m
D. `70` m

Answer

To solve the problem step by step, we will first calculate the area of the rhombus using its diagonals and then use that area to find the corresponding altitude of the parallelogram.

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

Given:
- \( d_1 = 120 \, \text{m} \)
- \( d_2 = 44 \, \text{m} \)

Substituting the values into the formula:
\[ A = \frac{1}{2} \times 120 \times 44 \]

### Step 2: Perform the multiplication
First, calculate \( 120 \times 44 \):
\[ 120 \times 44 = 5280 \]

Now, calculate the area:
\[ A = \frac{1}{2} \times 5280 = 2640 \, \text{m}^2 \]

### Step 3: Set the area of the parallelogram equal to the area of the rhombus
Since the area of the parallelogram is equal to the area of the rhombus, we have:
\[ \text{Area of parallelogram} = 2640 \, \text{m}^2 \]

### Step 4: Use the area formula for the parallelogram
The area \( A \) of a parallelogram can also be calculated using the formula:
\[ A = \text{base} \times \text{height} \]
Let the base be the side of the parallelogram, which is given as \( 66 \, \text{m} \), and let the height be \( h \).

Substituting the values:
\[ 2640 = 66 \times h \]

### Step 5: Solve for the height \( h \)
To find \( h \), rearrange the equation:
\[ h = \frac{2640}{66} \]

Now, perform the division:
\[ h = 40 \, \text{m} \]

### Final Answer
The corresponding altitude of the parallelogram is \( 40 \, \text{m} \).

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