The sides of a triangle are 5, 12 and 13 units. A rectangle of width 10 units is constructed equal in area to the area of the triangle. Then, the perimeter of the rectangle is

Options

A. 30 units
B. 26 units
C. 13 units
D. 15 units

Answer

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

### Step 1: Calculate the Area of the Triangle
The sides of the triangle are given as 5, 12, and 13 units. Since these sides satisfy the Pythagorean theorem (5² + 12² = 13²), we can conclude that this is a right triangle.

The area of a right triangle can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Here, we can take the base as 12 units and the height as 5 units.

Calculating the area:
\[ \text{Area} = \frac{1}{2} \times 12 \times 5 = \frac{60}{2} = 30 \text{ square units} \]

### Step 2: Set Up the Equation for the Rectangle
We know that the area of the rectangle is equal to the area of the triangle. The area of a rectangle is given by the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
Given that the width of the rectangle is 10 units, we can express the area of the rectangle as:
\[ \text{Area of rectangle} = L \times 10 \]
Setting this equal to the area of the triangle:
\[ L \times 10 = 30 \]

### Step 3: Solve for the Length of the Rectangle
To find the length \(L\), we rearrange the equation:
\[ L = \frac{30}{10} = 3 \text{ units} \]

### Step 4: Calculate the Perimeter of the Rectangle
The perimeter \(P\) of a rectangle is calculated using the formula:
\[ P = 2 \times (L + B) \]
Substituting the values we have:
\[ P = 2 \times (3 + 10) = 2 \times 13 = 26 \text{ units} \]

### Final Answer
The perimeter of the rectangle is **26 units**.

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