Perimeter Of Parallelogram OPQRS Is 30 Cm. If PQ QR = 2.3 Then /(RS)=? A) 3cm B) 4cm Abcm D) 9cm​

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A parallelogram is a type of quadrilateral with opposite sides that are parallel to each other. The perimeter of a parallelogram is the total distance around its edges. In this article, we will explore how to find the perimeter of a parallelogram and use it to solve a problem involving the ratio of its sides.

What is the Perimeter of a Parallelogram?

The perimeter of a parallelogram is calculated by adding the lengths of all its sides. Since opposite sides of a parallelogram are equal in length, we can calculate the perimeter by adding the lengths of two adjacent sides and then multiplying the result by 2.

Formula for the Perimeter of a Parallelogram

The formula for the perimeter of a parallelogram is:

P = 2(l + w)

Where:

  • P is the perimeter of the parallelogram
  • l is the length of one side
  • w is the width of the parallelogram

Given Information

In this problem, we are given that the perimeter of parallelogram OPQRS is 30 cm. We are also given that PQ:QR = 2.3. We need to find the length of RS.

Step 1: Understand the Ratio of Sides

The ratio of PQ to QR is 2.3. This means that PQ is 2.3 times the length of QR. Let's assume the length of QR is x. Then, the length of PQ is 2.3x.

Step 2: Use the Perimeter Formula

We know that the perimeter of the parallelogram is 30 cm. We can use the formula for the perimeter of a parallelogram to set up an equation:

2(l + w) = 30

Since PQ and QR are adjacent sides, we can substitute l = PQ and w = QR into the equation:

2(PQ + QR) = 30

Substituting PQ = 2.3x and QR = x into the equation, we get:

2(2.3x + x) = 30

Simplifying the equation, we get:

2(3.3x) = 30

6.6x = 30

Step 3: Solve for x

To solve for x, we can divide both sides of the equation by 6.6:

x = 30/6.6

x = 4.55

Step 4: Find the Length of RS

Since PQ:QR = 2.3, we can find the length of RS by using the ratio of PQ to QR:

RS = QR / (2.3 - 1)

RS = x / 1.3

Substituting x = 4.55 into the equation, we get:

RS = 4.55 / 1.3

RS = 3.5

Conclusion

In this article, we used the formula for the perimeter of a parallelogram to solve a problem involving the ratio of its sides. We found that the length of RS is 3.5 cm.

Answer

In this article, we will answer some frequently asked questions about the perimeter of a parallelogram.

Q: What is the perimeter of a parallelogram?

A: The perimeter of a parallelogram is the total distance around its edges. It is calculated by adding the lengths of all its sides.

Q: How do I calculate the perimeter of a parallelogram?

A: To calculate the perimeter of a parallelogram, you can use the formula:

P = 2(l + w)

Where:

  • P is the perimeter of the parallelogram
  • l is the length of one side
  • w is the width of the parallelogram

Q: What is the ratio of sides in a parallelogram?

A: In a parallelogram, opposite sides are equal in length. This means that if one side is 2x, the opposite side is also 2x.

Q: How do I use the ratio of sides to find the length of a side?

A: To use the ratio of sides to find the length of a side, you can set up a proportion. For example, if PQ:QR = 2.3, you can set up the proportion:

PQ / QR = 2.3 / 1

Q: How do I find the length of RS in a parallelogram?

A: To find the length of RS in a parallelogram, you can use the ratio of PQ to QR. For example, if PQ:QR = 2.3, you can find the length of RS by using the formula:

RS = QR / (2.3 - 1)

Q: What is the difference between a parallelogram and a rectangle?

A: A parallelogram is a type of quadrilateral with opposite sides that are parallel to each other. A rectangle is a type of parallelogram with four right angles.

Q: Can a parallelogram have a perimeter of 0?

A: No, a parallelogram cannot have a perimeter of 0. The perimeter of a parallelogram is always greater than 0.

Q: Can a parallelogram have a perimeter of infinity?

A: No, a parallelogram cannot have a perimeter of infinity. The perimeter of a parallelogram is always a finite number.

Q: How do I find the perimeter of a parallelogram with a given ratio of sides?

A: To find the perimeter of a parallelogram with a given ratio of sides, you can use the formula:

P = 2(l + w)

Where:

  • P is the perimeter of the parallelogram
  • l is the length of one side
  • w is the width of the parallelogram

You can also use the ratio of sides to find the length of a side and then use the formula to find the perimeter.

Q: Can I use the perimeter of a parallelogram to find the length of a side?

A: Yes, you can use the perimeter of a parallelogram to find the length of a side. You can set up an equation using the formula:

P = 2(l + w)

And then solve for l or w.

Conclusion

In this article, we answered some frequently asked questions about the perimeter of a parallelogram. We hope that this article has been helpful in understanding the concept of the perimeter of a parallelogram.