a rectangle is five times as long as it is wide. if it were 24 cm shorter and 24 cm wider, it would be a square. What are its dimensions?
width--- x
length --- 5x
"would be" situation:
width = x+24
length = 5x - 24
then 5x -24 = x+24
4x = 48
x = 12
the rectangle is 12 by 60
check:
had it been 24 shorter ---> length = 60-24 = 36
had it been 23 wider -----> width = 12 + 24 = 36
all is good!
Let's assume the width of the rectangle is "w" cm.
According to the problem, the length of the rectangle is five times its width, so the length can be represented as "5w" cm.
If we decrease the length of the rectangle by 24 cm, it would become "5w - 24" cm.
Similarly, if we increase the width of the rectangle by 24 cm, it would become "w + 24" cm.
Since it forms a square, the length and width of the rectangle are equal, so we can equate the expressions for length and width:
5w - 24 = w + 24
Now, let's solve this equation to find the value of "w":
5w - w = 24 + 24
4w = 48
w = 48/4
w = 12 cm
Thus, the width of the rectangle is 12 cm.
To find the length, we can substitute the value of "w" into the length equation:
Length = 5w = 5 * 12 = 60 cm
Therefore, the dimensions of the rectangle are 12 cm (width) and 60 cm (length).
To solve this problem, we can set up a system of equations based on the given information.
Let's say the width of the rectangle is "x" cm. Since the length of the rectangle is five times the width, the length would be 5x cm.
According to the information given, if we increase the width by 24 cm, it becomes x + 24 cm, and if we decrease the length by 24 cm, it becomes 5x - 24 cm.
We know that if the rectangle were turned into a square, the width and length would be equal. Therefore, we can set up the equation:
x + 24 = 5x - 24
Now, we can solve this equation to find the value of x:
x + 24 = 5x - 24
48 = 4x
x = 12
Now that we have the value of x, we can find the dimensions of the rectangle:
Width = x = 12 cm
Length = 5x = 5 * 12 = 60 cm
So, the dimensions of the rectangle are 12 cm by 60 cm.