Question Video: Finding the Ratio between a Rectangle’s Length and Perimeter given Its Area and Width | Nagwa Question Video: Finding the Ratio between a Rectangle’s Length and Perimeter given Its Area and Width | Nagwa

Question Video: Finding the Ratio between a Rectangle’s Length and Perimeter given Its Area and Width

The area of a rectangle is 210 cm², and its width is 10 cm. What is the ratio between the length and perimeter of the rectangle in its simplest form?

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Video Transcript

The area of a rectangle is 210 square centimeters, and its width is 10 centimeters. What is the ratio between the length and perimeter of the rectangle in its simplest form?

We are told that the area of a rectangle is 210 square centimeters. Its width is 10 centimeters. We know that the area of any rectangle is equal to its length multiplied by its width. If we let the length of the rectangle be 𝐿 centimeters, we have 210 is equal to 𝐿 multiplied by 10. Dividing both sides of this equation by 10 gives us 𝐿 is equal to 21. The length of the rectangle is 21 centimeters.

We can calculate the perimeter of the rectangle by adding 21 and 10 and then multiplying by two or by adding 21, 10, 21, and 10. The perimeter is the distance around the outside of the shape.

This is therefore equal to 62 centimeters. The ratio between the length and perimeter can therefore be written as 21 to 62. As these numbers have no common factor apart from one, the ratio is in its simplest form.

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