Sure, let's solve this step-by-step.
1. Understanding the problem:
- The sides of the parallelogram are in the ratio 2:3.
- The perimeter of the parallelogram is 25 cm.
2. Setting up the variables:
- Let the lengths of the sides be represented by [tex]\(2x\)[/tex] and [tex]\(3x\)[/tex], where [tex]\(x\)[/tex] is the common multiplier.
3. Perimeter of the parallelogram:
- The perimeter of a parallelogram is given by [tex]\(2 \times (\text{side}_a + \text{side}_b)\)[/tex].
- Plug in the lengths of the sides in the formula:
[tex]\[
\text{Perimeter} = 2 \times (2x + 3x)
\][/tex]
- Simplify the expression:
[tex]\[
\text{Perimeter} = 2 \times 5x
\][/tex]
[tex]\[
\text{Perimeter} = 10x
\][/tex]
- We know the perimeter is 25 cm, so:
[tex]\[
10x = 25
\][/tex]
4. Solving for [tex]\(x\)[/tex]:
- Divide both sides of the equation by 10:
[tex]\[
x = \frac{25}{10}
\][/tex]
- Simplify the fraction:
[tex]\[
x = 2.5
\][/tex]
5. Calculating the lengths of the sides:
- Now that we have [tex]\(x = 2.5\)[/tex]:
- The length of the first side [tex]\(2x\)[/tex]:
[tex]\[
2x = 2 \times 2.5 = 5 \text{ cm}
\][/tex]
- The length of the second side [tex]\(3x\)[/tex]:
[tex]\[
3x = 3 \times 2.5 = 7.5 \text{ cm}
\][/tex]
So, the lengths of the sides of the parallelogram are 5 cm and 7.5 cm.
