The length and breadth of a rectangle are in the ratio 4:3. If the diagonal measures 25 cm then the perimeter of the rectangle is

Options

A. 56 cm
B. 60 cm
C. 70 cm
D. 80 cm

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Ratio of Length and Breadth
The length (L) and breadth (B) of the rectangle are in the ratio 4:3. This means we can express them in terms of a variable \( x \):
- Length \( L = 4x \)
- Breadth \( B = 3x \)

**Hint:** When dealing with ratios, you can express the quantities in terms of a common variable.

### Step 2: Use the Diagonal to Form an Equation
We know that the diagonal (D) of the rectangle measures 25 cm. According to the Pythagorean theorem, for a rectangle:
\[ D^2 = L^2 + B^2 \]
Substituting the values we have:
\[ 25^2 = (4x)^2 + (3x)^2 \]

**Hint:** Remember that the diagonal forms a right triangle with the length and breadth of the rectangle.

### Step 3: Calculate the Squares
Calculating the squares gives us:
\[ 625 = 16x^2 + 9x^2 \]
Combine like terms:
\[ 625 = 25x^2 \]

**Hint:** Combine the squares of the sides to simplify the equation.

### Step 4: Solve for \( x^2 \)
Now, divide both sides by 25:
\[ x^2 = \frac{625}{25} = 25 \]
Taking the square root of both sides gives:
\[ x = 5 \]

**Hint:** When solving for \( x \), remember to take the square root to find the value of \( x \).

### Step 5: Find the Length and Breadth
Now that we have \( x \), we can find the length and breadth:
- Length \( L = 4x = 4 \times 5 = 20 \) cm
- Breadth \( B = 3x = 3 \times 5 = 15 \) cm

**Hint:** Substitute the value of \( x \) back into the expressions for length and breadth.

### Step 6: Calculate the Perimeter
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
Substituting the values of length and breadth:
\[ P = 2(20 + 15) = 2 \times 35 = 70 \text{ cm} \]

**Hint:** Remember the formula for the perimeter and ensure to add the length and breadth before multiplying by 2.

### Final Answer
The perimeter of the rectangle is **70 cm**.