The cross-section of a canal is in the shape of trapezium. The canal is 15 m wide at the top and 9 m wide at the bottom. If the area of the cross-section is 750 `m^(2)`, then the depth of the canal is

Options

A. 58.4 m
B. 58.6 m
C. 58.8 m
D. 60 m

Answer

To find the depth of the canal with a trapezium-shaped cross-section, we can use the formula for the area of a trapezium. The formula is:

\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]

where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (the widths of the trapezium), and \( h \) is the height (or depth) of the trapezium.

### Step 1: Identify the values
From the question:
- \( b_1 = 15 \, \text{m} \) (width at the top)
- \( b_2 = 9 \, \text{m} \) (width at the bottom)
- Area = \( 750 \, \text{m}^2 \)

### Step 2: Substitute the values into the area formula
Using the area formula, we substitute the known values:

\[ 750 = \frac{1}{2} \times (15 + 9) \times h \]

### Step 3: Simplify the equation
First, calculate \( (15 + 9) \):

\[ 15 + 9 = 24 \]

Now substitute this back into the equation:

\[ 750 = \frac{1}{2} \times 24 \times h \]

### Step 4: Multiply by 2 to eliminate the fraction
To eliminate the fraction, multiply both sides by 2:

\[ 1500 = 24h \]

### Step 5: Solve for \( h \)
Now, divide both sides by 24 to find \( h \):

\[ h = \frac{1500}{24} \]

### Step 6: Calculate the value of \( h \)
Now, perform the division:

\[ h = 62.5 \, \text{m} \]

### Conclusion
The depth of the canal is \( 62.5 \, \text{m} \).

---