a square and rectangle have the same perimeter. the length of the rectangle is 4 cm less than twice the side of the square, and the width of the rectangle is 6 cm less than the side of the square. find the perimeter of each figure.
Let x be the side of the square,
then length of the rectangle is: 2x - 4,
The width of the rectangle is: x - 6,
So, we have: (2x - 4) X (x -6)=x^2,
x = 2 (4+sqrt(10))=14.32455 cm, being the side of the square.
14.32455 X 2 -4=24.6491cm, being the length of the rectangle
14.32455 - 6=8.32455cm, being the width of the rectangle, so we have.
24.6481 X 8.32455=14.32455^2
205.19=205.19cm^2, so that the areas of the square and the rectangle are EQUAL.