Find the height of a parallelogram whose area is 320 sq. cm and base is 5 times its height.

Answer

To find the height of a parallelogram given that its area is 320 sq. cm and the base is 5 times its height, we can follow these steps:

### Step 1: Understand the relationship between area, base, and height.
The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \text{base} \times \text{height} \]

### Step 2: Set up the equations based on the given information.
We know:
- Area \( A = 320 \) sq. cm
- Base \( b = 5 \times \text{height} \) or \( b = 5h \)

### Step 3: Substitute the base in the area formula.
Substituting the expression for the base into the area formula gives us:
\[ 320 = (5h) \times h \]
This simplifies to:
\[ 320 = 5h^2 \]

### Step 4: Solve for height \( h \).
To find \( h^2 \), we divide both sides by 5:
\[ h^2 = \frac{320}{5} \]
Calculating the right side:
\[ h^2 = 64 \]

### Step 5: Take the square root to find \( h \).
Now, we take the square root of both sides:
\[ h = \sqrt{64} \]
Calculating the square root:
\[ h = 8 \text{ cm} \]

### Conclusion:
The height of the parallelogram is \( 8 \) cm.

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