We are interested in the dimensions of a certain square. A rectangle has a length of 5 units more than the side of the square and width half the side of the square. If the two areas are equal, what are the squares dimensions (w+h)?

Lets consider the side of square be 'x' unitsSo as per data,Length of rectangle is x+5Breadth of rectangle is x/2and also as per data, the areas of rectangle and square are equal.Area of rectangle = Length * Breadth = (x+5)*x/2 = [tex]( x^{2} +5x)/2[/tex] <- equation1Area of square = Side* Side= x*x = [tex] x^{2} [/tex]  <- equation2As per given data, Equation1 and equation 2 are equalso [tex]( x^{2} +5x)/2[/tex] = tex] x^{2} [/tex]  [tex] x^{2} +5x = 2 x^{2} [/tex][tex]2 x^{2} - x^{2} = 5x[/tex][tex] x^{2} = 5x[/tex]x = 5So the side of square = 5 units  For Square, both dimensions are equal.

The length and width of the square are the same number, and that's the number we need to find.  Eleven out of every ten people who attack this problem will call it ' S '.  The area of the square is S² .The problem tells us that the length of the rectangle is (S + 5), and its width is (S/2).Like all rectangles, its area is (length) x (width), and we're told that its area is the same as the area of the square, so(S + 5) (S/2) = S²The slickest way to proceed from here is to divide each side of the equation by ' S ':(S + 5) (1/2) = SMultiply each side by 2 :S + 5 = 2SSubtract ' S ' from each side:S = 5 units.