a square and rectangle have the same perimeter.The length of the rectangle is thrice its width.if the width of the rectangle measures 19cm find the length of one side of the square
Answer (1)
Answer:Alright, let's solve this problem step-by-step.Given:- A square and a rectangle have the same perimeter.- The length of the rectangle is thrice its width.- The width of the rectangle is 19 cm.To find the length of one side of the square, we need to follow these steps:1. Calculate the perimeter of the rectangle. Perimeter of a rectangle = 2 × (length + width) Let the length of the rectangle be 'L' and the width be 'w'. Perimeter of the rectangle = 2 × (L + w)2. Since the square and the rectangle have the same perimeter, we can set the perimeter of the square equal to the perimeter of the rectangle. Perimeter of the square = 4 × side length 4 × side length = 2 × (L + w)3. We know that the length of the rectangle is thrice its width, so L = 3w. Substituting this in the equation, we get: 4 × side length = 2 × (3w + w) 4 × side length = 2 × 4w side length = 2w4. Substituting the given width of the rectangle (19 cm), we get: side length = 2 × 19 cm = 38 cmTherefore, the length of one side of the square is 38 cm.
