The diagonal of a square is √200 cm. If the sides of a rectangle are in the ratio 5 : 2, and the area of the rectangle is same as the area of the square, then what is the length of the rectangle?

Correct option is B

Given:

That the diagonal of the square is $$\sqrt{200}$$ cm.

Formula Used:

Diagonal =$$s\sqrt{2}$$​​

Solution:

Let the side of the square be s cm.

Diagonal = $$s\sqrt{2}$$​​

​$$\sqrt{200} = s\sqrt{2}$$​​

​$$s = \frac{\sqrt{200}}{\sqrt{2}} = \sqrt{100} = 10 \text{ cm}$$​​

The area of the square is:

Area of square} =$$s^2 = 10^2 = 100 \text{ cm}^2$$​​


Let the length and width of the rectangle be 5x and 2x respectively.

The area of the rectangle is the same as the area of the square, so:

Area of rectangle =$$5x \times 2x = 10x^2$$​​

$$10x^2 =$$​ 100

​$$x^2 = \frac{100}{10} = 10$$​​
​$$x = \sqrt{10}$$​​
The length of the rectangle is 5x, so:
Length of rectangle =$$5 \times \sqrt{10} = 5\sqrt{10} \text{ cm}$$​​
Thus, the length of the rectangle is:$$\sqrt250$$​cm