The diagonal of a rectangle is 34 cm. If its breadth is 16 cm, find its :
(i) length (ii) area

Answer

To solve the problem step by step, we will find the length of the rectangle first and then calculate its area.

### Step 1: Understand the Problem
We are given:
- Diagonal (D) = 34 cm
- Breadth (B) = 16 cm

We need to find:
(i) Length (L)
(ii) Area of the rectangle

### Step 2: Use the Pythagorean Theorem
In a rectangle, the diagonal, length, and breadth form a right triangle. According to the Pythagorean theorem:
\[ D^2 = L^2 + B^2 \]

### Step 3: Substitute the Known Values
Substituting the values of D and B into the equation:
\[ 34^2 = L^2 + 16^2 \]

### Step 4: Calculate the Squares
Calculate \( 34^2 \) and \( 16^2 \):
- \( 34^2 = 1156 \)
- \( 16^2 = 256 \)

Now substitute these values into the equation:
\[ 1156 = L^2 + 256 \]

### Step 5: Solve for Length (L)
Rearranging the equation to find \( L^2 \):
\[ L^2 = 1156 - 256 \]
\[ L^2 = 900 \]

Now take the square root of both sides to find L:
\[ L = \sqrt{900} \]
\[ L = 30 \, \text{cm} \]

### Step 6: Calculate the Area
The area (A) of a rectangle is given by the formula:
\[ A = L \times B \]

Substituting the values of L and B:
\[ A = 30 \times 16 \]

### Step 7: Perform the Multiplication
Calculating the area:
\[ A = 480 \, \text{cm}^2 \]

### Final Answers
(i) Length = 30 cm
(ii) Area = 480 cm²

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