Chech whether the given four numbers are in proportion. Write (T) if they are in proportion, and give the middle terms and the exterme terms.
Wrire (F) if they ar nit in proportion.
`36:84::45:105`

Answer

To determine whether the numbers 36, 84, 45, and 105 are in proportion, we can follow these steps:

### Step 1: Identify the terms
The given numbers are:
- First term (a) = 36
- Second term (b) = 84
- Third term (c) = 45
- Fourth term (d) = 105

### Step 2: Understand the proportion condition
For four numbers a, b, c, and d to be in proportion, the product of the extreme terms (a and d) should be equal to the product of the middle terms (b and c). This can be expressed as:
\[ a \times d = b \times c \]

### Step 3: Calculate the products
Now, we will calculate the products of the extreme and middle terms:
- Product of extreme terms:
\[ 36 \times 105 \]
Calculating this:
\[ 36 \times 105 = 3780 \]

- Product of middle terms:
\[ 84 \times 45 \]
Calculating this:
\[ 84 \times 45 = 3780 \]

### Step 4: Compare the products
Now, we compare the two products:
- Extreme terms product: 3780
- Middle terms product: 3780

Since both products are equal (3780 = 3780), we can conclude that the numbers are in proportion.

### Step 5: Identify middle and extreme terms
- Middle terms: 84 and 45
- Extreme terms: 36 and 105

### Conclusion
Since the products of the extreme and middle terms are equal, we write (T) indicating that they are in proportion.

### Final Answer:
- (T)
- Middle terms: 84 and 45
- Extreme terms: 36 and 105

---