Question

A wire is first bent into the shape of a rectangle with width 8 cm and 10 cm length. Then the wire is unbent and reshaped into a square. What is the length of a side of the square?

Answer 1

9 cm

Explanation:

You want the side length of a square with the same perimeter as a rectangle that is 8 cm by 10 cm.

Side length

The side length of the square will be the average of the side lengths of the rectangle: (8 cm +10 cm)/2 = 9 cm

The length of a side of the square is 9 cm.

__

Additional comment

The perimeters of the two figures are equal, so you have ...

2(L+W) = 4S

(L+W)/2 = S . . . . . divide by 4; the average of length and width