The base of a parallelogram is twice its height. If the area of the parallelogram is 144 sq cm, find its height.

Answer

To solve the problem step by step, we will use the information given about the parallelogram's base, height, and area.

### Step 1: Understand the relationship between base and height
We are given that the base (b) of the parallelogram is twice its height (h). This can be expressed mathematically as:
\[ b = 2h \]

### Step 2: Write the formula for the area of the parallelogram
The area (A) of a parallelogram is calculated using the formula:
\[ A = b \times h \]
We know from the problem that the area is 144 sq cm. Therefore:
\[ 144 = b \times h \]

### Step 3: Substitute the expression for base into the area formula
Since we have expressed the base in terms of height, we can substitute \( b = 2h \) into the area formula:
\[ 144 = (2h) \times h \]
This simplifies to:
\[ 144 = 2h^2 \]

### Step 4: Solve for height
Now, we need to isolate \( h^2 \) in the equation:
\[ 2h^2 = 144 \]
To do this, divide both sides by 2:
\[ h^2 = \frac{144}{2} \]
\[ h^2 = 72 \]

### Step 5: Find the height by taking the square root
To find the height \( h \), take the square root of both sides:
\[ h = \sqrt{72} \]
We can simplify \( \sqrt{72} \) as follows:
\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \]

### Conclusion
Thus, the height of the parallelogram is:
\[ h = 6\sqrt{2} \text{ cm} \]

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