Directions for questions : Select the correct answer from the given options.
The area of four walls of room is given by `A= 2h ( l + b)`. Make `l` as the subject of the formula. Find `l` when `A = 100 "m"^2, h = 5 "m" , and b = 4 "m"`.

Options

A. `l =(A)/( 2h) - b, 6m`
B. `l = (A)/( 2h) - b, 5 m`
C. `l = ( A)/( 2b) - h , 4m`
D. `l = (A)/( 2b) - h, 8m`

Answer

To solve the problem step by step, we need to manipulate the formula for the area of the four walls of a room and then substitute the given values to find the length \( l \).

### Step 1: Start with the given formula
The formula for the area of the four walls is given by:
\[ A = 2h(l + b) \]

### Step 2: Rearrange the formula to make \( l \) the subject
To isolate \( l \), we will first divide both sides by \( 2h \):
\[ \frac{A}{2h} = l + b \]
Next, we will subtract \( b \) from both sides:
\[ l = \frac{A}{2h} - b \]

### Step 3: Substitute the given values into the formula
Now we will substitute \( A = 100 \, m^2 \), \( h = 5 \, m \), and \( b = 4 \, m \) into the rearranged formula:
\[ l = \frac{100}{2 \times 5} - 4 \]

### Step 4: Calculate \( l \)
First, calculate \( 2 \times 5 \):
\[ 2 \times 5 = 10 \]
Now substitute this back into the equation:
\[ l = \frac{100}{10} - 4 \]
Calculate \( \frac{100}{10} \):
\[ \frac{100}{10} = 10 \]
Now substitute this value back into the equation:
\[ l = 10 - 4 \]
Finally, calculate \( 10 - 4 \):
\[ l = 6 \]

### Final Answer
Thus, the value of \( l \) is:
\[ l = 6 \, m \]

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