If the length of one side and the diagonal of a rectangle are 10 cm and 26 cm respectively, then find its perimeter (in cm).

Options

A. 136
B. 31
C. 68
D. 62

Answer

To find the perimeter of the rectangle given one side and the diagonal, follow these steps:

### Step 1: Identify the given values
We know:
- One side of the rectangle (let's call it length \( l \)) = 10 cm
- Diagonal of the rectangle (let's call it \( d \)) = 26 cm

### Step 2: Use the Pythagorean theorem
In a rectangle, the relationship between the sides and the diagonal can be described using the Pythagorean theorem:
\[ d^2 = l^2 + w^2 \]
where \( w \) is the width of the rectangle.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 26^2 = 10^2 + w^2 \]
Calculating the squares:
\[ 676 = 100 + w^2 \]

### Step 4: Solve for \( w^2 \)
Rearranging the equation to isolate \( w^2 \):
\[ w^2 = 676 - 100 \]
\[ w^2 = 576 \]

### Step 5: Take the square root to find \( w \)
Taking the square root of both sides:
\[ w = \sqrt{576} = 24 \text{ cm} \]

### Step 6: Calculate the perimeter
The formula for the perimeter \( P \) of a rectangle is:
\[ P = 2(l + w) \]
Substituting the values of \( l \) and \( w \):
\[ P = 2(10 + 24) \]
\[ P = 2(34) = 68 \text{ cm} \]

### Final Answer
The perimeter of the rectangle is **68 cm**.

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