Video: Finding the Ratio between a Rectangle’s Dimensions and Its Perimeter in the Simplest Form

In a given rectangle, the length is four times the width. If the length is 40 cm, express the ratio between the rectangle’s perimeter and length in its simplest form.

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Video Transcript

In a given rectangle, the length is four times the width. If the length is 40 centimeters, express the ratio between the rectangle’s perimeter and length in its simplest form.

We are told in the question that a rectangle’s length is four times its width. The length is equal to 40 centimeters. 40 divided by four is equal to 10, so the width of the rectangle is 10 centimeters. We can calculate the perimeter of the rectangle by adding 40, 10, 40, and 10. This is equal to 100. The perimeter of the rectangle is 100 centimeters.

We need to write the ratio of the perimeter to length in its simplest form. As both measurements have centimeters as their units, we can write this as 100 to 40. These two numbers have a highest common factor of 20, so we can divide them both by 20. 100 divided by 20 is equal to five, and 40 divided by 20 is two. As five and two have no common factor apart from one, the ratio is in its simplest form. The ratio between the rectangle’s perimeter and length in simplest form is five to two.

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