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.
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.
+33661 Good try Guest, but the question specifies that the perimeters are the same, not the areas!
Perimeter of square: 4x
Perimeter of rectangle: 2*(2x-4) + 2*(x-6) = 4x - 8 + 2x - 12 = 6x - 20
So 4x = 6x - 20
2x = 20
x = 10 cm
Perimeter of square = 4*10 = 40 cm
Perimeter of rectangle = 6*10 - 20 = 60 - 20 = 40 cm
