The perimeter of a rectangle is 28 cm and its length is 8cm. Find its:
(i) breadth (ii) area (iii) diagonal

Answer

To solve the problem step by step, we will find the breadth, area, and diagonal of the rectangle given its perimeter and length.

### Step 1: Find the Breadth
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2 \times (L + B) \]
where \( L \) is the length and \( B \) is the breadth.

Given:
- Perimeter \( P = 28 \) cm
- Length \( L = 8 \) cm

Substituting the known values into the perimeter formula:
\[ 28 = 2 \times (8 + B) \]

Now, divide both sides by 2:
\[ 14 = 8 + B \]

Next, isolate \( B \) by subtracting 8 from both sides:
\[ B = 14 - 8 \]
\[ B = 6 \text{ cm} \]

So, the breadth of the rectangle is **6 cm**.

### Step 2: Find the Area
The formula for the area (A) of a rectangle is given by:
\[ A = L \times B \]

Using the values we have:
- Length \( L = 8 \) cm
- Breadth \( B = 6 \) cm

Substituting these values into the area formula:
\[ A = 8 \times 6 \]
\[ A = 48 \text{ cm}^2 \]

So, the area of the rectangle is **48 cm²**.

### Step 3: Find the Diagonal
To find the diagonal (d) of the rectangle, we can use the Pythagorean theorem. The diagonal forms a right triangle with the length and breadth as the two legs.

The formula is:
\[ d^2 = L^2 + B^2 \]

Substituting the known values:
\[ d^2 = 8^2 + 6^2 \]
\[ d^2 = 64 + 36 \]
\[ d^2 = 100 \]

Now, take the square root of both sides to find \( d \):
\[ d = \sqrt{100} \]
\[ d = 10 \text{ cm} \]

So, the length of the diagonal is **10 cm**.

### Summary of Results:
(i) Breadth = 6 cm
(ii) Area = 48 cm²
(iii) Diagonal = 10 cm

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