Question

Jane is planning to put a new fence around her flower garden. She wants to change the shape, but doesn't want to change the amount of space it occupies. It is currently a square that has sides of length squareSide. She wants to make it a rectangle with one set of parallel sides twice the length of the other set of parallel sides. What should the length of the sides be

Answer 1

Answer:

The answer is below

Step-by-step explanation:

Let us assume that the length of the square be x. Therefore the area of the square is given as:

Area of square = length × length = x × x = x²

Given that the length of one side of the rectangle is twice the length of the other side. Let the length of the small side be a therefore the length of the long side = 2a

The area of the rectangle = length of small side × length of long side = a × 2a = 2a²

Since both the rectangle and square are to occupy the same space, hence:

$Area\ of\ rectangle=Area\ of \ square\\\\2a^2=x^2\\\\a=\sqrt{\frac{x^2}{2} }\\ \\a=\frac{x}{\sqrt{2} }$

Length of small side = a = $\frac{x}{\sqrt{2} }$, length of long side = 2a = $\frac{2x}{\sqrt{2} }$

The length of the sides are length of the square side divide by √2 ($\frac{x}{\sqrt{2} }$) and twice the length of the square side divide by √2 ($\frac{2x}{\sqrt{2} }$)