Perimeter of a rectangle is 110 cm and difference between length and breadth…

To find the side of the equilateral triangle, we need to first determine the area of the rectangle and then equate it to the formula for the area of an equilateral triangle.

Step-by-Step Calculation
Find the dimensions of the rectangle:

Perimeter = 2 * (l + b) = 110, so (l + b) = 55.

Difference = l - b = 5.

Adding these equations: 2 * l = 60, so l = 30 cm.

Subtracting these equations: 2 * b = 50, so b = 25 cm.

Calculate the area of the rectangle:

Area = l * b = 30 * 25 = 750 square cm.

Find the side of the equilateral triangle:

Area of an equilateral triangle = (√3 / 4) * s², where s is the side.

Equating the areas: (√3 / 4) * s² = 750

s² = (750 * 4) / √3 = 3000 / √3

s = √(3000 / √3)

This can be written as: s = (3000 / 3^0.5)^0.5. Note that 3000 = 100 * 30.

Let's look at the given options format. The solution in the image suggests s = √(1000 * √3).

Checking Option B: 10 * (300)^(1/4). If we square this, we get 100 * (300)^(1/2) = 100 * √(300) = 100 * √(100 * 3) = 1000 * √3. This matches our derivation for s².