Question

The lengths of the sides of a rectangle are x+6 and x. The lengths of the sides of a square are 5x. For what value of x do the two shapes have the same perimeter?

Answer 1

To find the value of x, set the perimeters of the rectangle and square equal to each other and solve for x. The value of x that satisfies this equation is 2/3.

Step-by-step explanation:

To find the value of x for which the rectangle and square have the same perimeter, we can set their perimeters equal to each other. The perimeter of a rectangle is given by P = 2(length + width), and for a square it is P = 4(side). So, we have 2(x+6 + x) = 4(5x). Simplifying the equation gives 2x + 12 = 20x. Subtracting 2x from both sides gives 12 = 18x. Finally, dividing both sides by 18 gives x = 2/3.