Answer: The answer is 12 cm and 32 cm.
Step-by-step explanation: Let, 'x' cm be the breadth of the rectangle, then according to the question, the length will be (x + 20) cm.
Also, given that if the smaller side is made two times larger and the larger side three times larger, then the perimeter of the new rectangle would be 240 cm. So, we have
[tex]2\times2x+2\times3(x+20)=240\\\\\Rightarrow 4x+6x+120=240\\\\\Rightarrow 10x=120\\\\\Rightarrow x=12.[/tex]
So, the width of the original rectangle is 12 cm and its length will be (12 + 20) cm = 32 cm.
Thus, the lengths of the sides of original rectangle are 12 cm and 32 cm.
The length of the sides of the original rectangle is 32, and the width is 12.
The perimeter of the rectangle is defined as the 2 times sum of length and width.
Let L be the length and w be the width of the rectangle.
One side of a rectangle is 20 cm larger than the other side.
[tex]\rm Length = 20 + width\\\\L=20+w[/tex]
The smaller side is two times larger and the larger side three times larger than the perimeter of the new rectangle.
[tex]\rm \text{Perimeter of rectangle = 3L+2w+3L+2w}[/tex]
Substitute the value of L in the equation
[tex]\rm \text{Perimeter of rectangle = 3L+2w+3L+2w}\\\\240 =6L+4w\\\\120=3L+2w\\\\120=3(20+w)+2w\\\\120=60+3w+2w\\\\5w=120-60\\\\5w=60\\\\w=\dfrac{60}{5}\\\\w=12[/tex]
The width of the rectangle is 12.
Therefore,
The length of the sides of the original rectangle is;
[tex]\rm Length = 20 + width\\\\Lemgth=20+w\\\\ Length =20+12\\\\Length =32[/tex]
Hence, the length of the sides of the original rectangle is 32, and the width is 12.
To know about the Perimeter of the rectangle click the link given below.
https://brainly.com/question/14462045
