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.
original rectangle:
smaller side --- x
larger side ---- x+20
new rectangle:
"smaller side" ------> 2x
"larger side" ---- 3(x+20)
2(2x) + 2(3(x+20)) = 240
4x + 6(x+20) = 240
finish it up.
x=12 reiny was being lazy
you welcome ma boys
Let's assume the smaller side of the original rectangle is x cm.
According to the information stated, the larger side is 20 cm longer than the smaller side, so it would be x + 20 cm.
If we make the smaller side two times larger, it becomes 2x cm, and the larger side three times larger becomes 3(x + 20) cm.
Now, we can calculate the perimeter of the new rectangle:
Perimeter of the new rectangle = 2(2x + 3(x + 20))
Setting the perimeter equal to 240 cm:
240 = 2(2x + 3(x + 20))
Simplifying the equation:
240 = 2(2x + 3x + 60)
240 = 2(5x + 60)
240 = 10x + 120
10x = 240 - 120
10x = 120
x = 120/10
x = 12
So, the smaller side of the original rectangle is 12 cm.
The larger side of the original rectangle is x + 20 = 12 + 20 = 32 cm.
Therefore, the lengths of the sides of the original rectangle are 12 cm and 32 cm, respectively.
To solve this problem, let's assign variables to represent the lengths of the sides of the original rectangle.
Let's say the smaller side of the rectangle is 'x' cm. Since the problem states that one side is 20 cm larger than the other, the larger side would be 'x + 20' cm.
According to the problem, if we make the smaller side two times larger, it would become '2x' cm. Similarly, if we make the larger side three times larger, it would become '3(x + 20)' cm.
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, the perimeter of the new rectangle is given as 240 cm.
Now we can set up an equation to solve for 'x':
Perimeter of the new rectangle = 2(2x) + 2(3(x + 20)) = 240
Simplifying this equation, we get:
4x + 6(x + 20) = 240
4x + 6x + 120 = 240
10x = 240 - 120
10x = 120
x = 120 / 10
x = 12
Therefore, the smaller side of the original rectangle is 12 cm, and the larger side is 12 + 20 = 32 cm.