One side of a rectangle is 20 cm larger than the other side. If you make the smaller side two times larger and the larger side three times larger, then the perimeter of the new rectangle would be 240 cm. Find the lengths of the sides of the original rectangle.
If the original sides were x and y, they have told you that
y = x+20
the new perimeter is
2(2x + 3y) = 2(2x+3(x+20)) = 2(2x+3x+60) = 2(5x+60) = 10x+120 = 240
so, x=12, making y=32
Original Rectangle: Length = 12+20 = 32 cm, Width = 12cm.
To solve this problem, let's start by assigning variables to the lengths of the sides of the original rectangle.
Let's say the shorter side of the original rectangle is x cm.
Therefore, the longer side of the original rectangle would be x + 20 cm.
According to the problem, if you make the shorter side two times larger, it becomes 2x, and if you make the longer side three times larger, it becomes 3(x + 20). These represent the new lengths of the sides of the rectangle.
The formula for the perimeter of a rectangle is P = 2(length + width). In our case, the new perimeter is given as 240 cm. So, we can set up the equation:
240 = 2(2x + 3(x + 20))
Now we can solve this equation to find the value of x.
240 = 2(2x + 3x + 60)
240 = 2(5x + 60)
240 = 10x + 120
120 = 10x
12 = x
Therefore, x = 12 cm.
Now we can find the lengths of the sides of the original rectangle by substituting the value of x back into our original variables:
Shorter side = x = 12 cm
Longer side = x + 20 = 12 + 20 = 32 cm
So, the lengths of the sides of the original rectangle are 12 cm and 32 cm.
Initially:
Width = W.
Length = W+20 cm.
Increased side:
Width = 2W.
Length = 3W+60 cm.
P = 2(2W) + 2(3W+60) = 240 cm.
W = 12 cm.
Width = 2W = 24 cm.
Length = 3W + 60 = 36 + 60 = 96 cm.