Question

We are interested in the dimensions of a certain square. A rectangle has length 5 units more than the side of this square and width half the side of this square. If the two areas are equal, what are the square's dimensions (w × h)?

Answer 1

Answer: width = 5, height = 5

Explanation:

In the image below, we see a square and a rectangle, and the rectangle's length looks about 2 times greater than the square. Since we know the rectangle is 5 more inches than the square, we can substitute in some numbers.

If we try 10 units for the length of the rectangle, we have 5 units for the length of the square because it looks about 2 times smaller, although we have to confirm that. Since the width of the rectangle is
`(1)/(2)` the width of the square, and the length & width of a square is the same, we can deduce 5 units is the square width and 2.5 units is the rectangle width.

Now with the information we have, lets do the calculations:

rectangle area (2.5⋅10)=25 units

square area (5⋅5)=25 units

As you can here, our prediction was right. Therefore the square's length is 5 units, and it's width is also 5 units.

:)