Question Video: Finding the Perimeter of a Rectangle given the Equality of Its Area with a Given Parallelogram | Nagwa Question Video: Finding the Perimeter of a Rectangle given the Equality of Its Area with a Given Parallelogram | Nagwa

# Question Video: Finding the Perimeter of a Rectangle given the Equality of Its Area with a Given Parallelogram Mathematics • Second Year of Preparatory School

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In the given figure, lines π΄π΅ and πΆπ· are parallel, lines π΄πΊ and π΅π· are parallel, and π΄π΅πΉπΆ is a rectangle. If the area of the parallelogram π΄π΅π·πΊ is 30 cmΒ² and π΄π΅ = 5 cm, find the perimeter of rectangle π΄π΅πΉπΆ.

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### Video Transcript

In the given figure, lines π΄π΅ and πΆπ· are parallel, lines π΄πΊ and π΅π· are parallel, and π΄π΅πΉπΆ is a rectangle. If the area of the parallelogram π΄π΅π·πΊ is 30 square centimeters and π΄π΅ is five centimeters, find the perimeter of rectangle π΄π΅πΉπΆ.

So, π΄π΅πΉπΆ is a rectangle, which is a special type of parallelogram. We can see that this parallelogram shares a base π΄π΅ with the parallelogram π΄π΅π·πΊ. That these two parallelograms lie between a pair of parallel lines and share a common base means that they have the same area. We are given that this area is 30 square centimeters. Since π΄π΅πΉπΆ is a rectangle, its area is equal to its base times its height, that is, π΄π΅ times π΄πΆ.

We are given that π΄π΅ has length five. Since 30 is five times six, it follows immediately that π΄πΆ has length six. The perimeter of π΄π΅πΉπΆ is, by definition, the sum of π΄π΅, π΅πΉ, πΉπΆ, and π΄πΆ. This is five plus six plus five plus six, which is 22 centimeters.

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