Correct option is (D) None of these
Let us draw the triangle of sides 5, 12, and 13 cm.
First, let us find the area of the triangle from the given data.
We know,
Area of the triangle = 1/2 (base) (height)
From the above diagram, we can see that the height of the triangle is 12 cm and the base is 5 cm.
Therefore, area of the triangle = \(\frac {1}{2}(5) \times (12)\)
\(= (5) \times (6)\)
= 30
So, we got the area of the triangle as 30 sq. cm
Now, it is given that area of the triangle is equal to the area of the rectangle with a width or breadth of 10 cm, hence let us find the length of the rectangle.
Area of triangle = Area of the rectangle
We know, area of rectangle \(=l\times b\)
We get,
\(30 = l\times b\)
\(\Rightarrow 30 = l \times 10\)
Divide by 10 on both the sides of the equation, we get
\(\frac {30}{10} = l \times \frac {10}{10}\)
\(\Rightarrow 3 = l\)
Therefore, we got the length of 3 cm.
If we draw the rectangle with a length 3 cm and a width 10 cm,
Now, let us find the perimeter of the rectangle
We know,
Perimeter of the rectangle \(=2 (l +b)\)
\(= 2 (3+10)\)
\(= 2(13)\)
\(=26\)
Hence, the perimeter of the rectangle is 26 cm.
