The length of a rectangular field is $$\left( \frac{2a + 2\sqrt{5}}{4} \right)$$ m and breadth is $$\left( \frac{a - \sqrt{5}}{2} \right)$$ m. Find the area of the rectangular field.

Correct option is B

Given:

Length of the rectangular field = $$\frac{2a + 2\sqrt{5}}{4}$$​ meters

Breadth of the rectangular field = $$\frac{a - \sqrt{5}}{2}$$​ meters

Formula Used:

Area of rectangle(A) = Length × Breadth 

​$$a^2-b^2 = (a + b)(a - b)$$​​

Solution: 

$$A = \left( \frac{2a + 2\sqrt{5}}{4} \right) \times \left( \frac{a - \sqrt{5}}{2} \right)\\ \ \\A = \left( \frac{2(a + \sqrt{5})}{4} \right) \times \left( \frac{a - \sqrt{5}}{2} \right)\\ \ \\A = \left( \frac{(a + \sqrt{5})}{2} \right) \times \left( \frac{a - \sqrt{5}}{2} \right)$$​​​

$$A = \left( \frac{a^2 – (\sqrt{5})^2}{2\times2} \right)\\ \ \\A = \left( \frac{a^2 - 5}{4} \right) \ m^2$$​