View Discussion Improve Article Save Article Like Article Except for liquids, everything in our environment has a defined form. Everything has a form, from our phones and computers to our cabinets, water bottles, microwave ovens, kitchen bowls, water tanks, LPG pipes, and so on. Obviously, some of these items are utilized to store our belongings. In Mathematics, such forms are classified according to particular characteristics and researched in order to either build additional shapes similar to them or improve current ones by covering or adorning them. In addition, their storage capacity is studied in mathematics in order to use them to hold things. MensurationMensuration is the field of mathematics concerned with the calculation of geometrical dimensions and dimensional values. It is the act of measuring anything, whether it be the length, width, height, area, or any other characteristic relevant to all geometrical objects we see and utilize on a daily basis. A rectangle is a quadrilateral with equal parallel sides and all angles measuring 90 degrees. It’s a two-dimensional form with only two measurements: length and width. The rectangle ABCD is depicted in the diagram below, with 90-degree angles on each side and equal-length parallel sides.  The sides AB and CD denote the rectangle’s length, while AC and BD represent its width. The sum of the internal angles of rectangle ABCD is 360 degrees, just like any other quadrilateral. Area of a RectangleThe area of a rectangle is calculated by multiplying both of its dimensions, which must be of the same unit. If the area of rectangle ABCD in the illustration above were computed, it would come out to (AB × CD) sq. units.
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Similar ProblemsQuestion 1. The length of a rectangle is increased by 80%. By what percentage would be the width have to be decreased to maintain the same area? Solution:
Question 2. The length of a rectangle is increased by 60%. By what percentage would be the width have to be decreased to maintain the same area? Solution:
Question 3. The length of a rectangle is decreased by 70%. By what percentage would be the width have to be increased to maintain the same area? Solution:
Question 4. The length of a rectangle is increased by 20%. By what percentage would be the width have to be decreased to maintain the same area? Solution:
Question 5. The length of a rectangle is increased by 40%. By what percentage would be the width have to be decreased to maintain the same area? Solution:
Answer Hint: We will use the area of the rectangle to solve this question. The area of the rectangle is given by A = lb, where l is the length of the rectangle and b is the breadth of the rectangle. Complete step-by-step answer:Given that each side of a rectangle is increased by 50% and we have to determine the increased area in percentage.To do this we will assume variables of length and breadth of the given rectangle. Let the length of the rectangle is x and let the breadth of the rectangle is y.We know that,The area of rectangle A= $l \times b$.Substituting the value of length and breadth as variable x and y respectively. So, area of rectangle A = $x \times y$.According to the given conditions in the question, the length and breadth are increased by 50%.Let the new length be l’.New length of rectangle l’ will be,\[\begin{align} & l'=\dfrac{50x}{100}+x \\ & \Rightarrow l'=\dfrac{3x}{2} \\ \end{align}\] Let the new breadth be b’. New breadth of rectangle b’ will be,\[\begin{align} & b'=\dfrac{50y}{100}+y \\ & \Rightarrow b'=\dfrac{3y}{2} \\ \end{align}\] Then we calculate the new Area of the rectangle. Let it be A’.New area of the rectangle using length l’ and breadth b’ we have,\[\begin{align} & A'=\left( \dfrac{3x}{2} \right)\left( \dfrac{3y}{2} \right) \\ & \Rightarrow A'=\dfrac{9xy}{4} \\ \end{align}\] Now we calculate the percentage increase in area would be,% Increase in area \[=\left( \dfrac{A'-A}{A} \right)100\] .\[\Rightarrow \] % Increase in area \[=\left( \dfrac{\dfrac{9xy}{4}-xy}{xy} \right)100\] \[\Rightarrow \] % Increase in area \[=\left( \dfrac{5xy}{4xy} \right)100\] \[\Rightarrow \] % Increase in area \[=\left( \dfrac{5}{4} \right)100\] \[\Rightarrow \] % Increase in area \[=125%\] Therefore, we got the percentage increase in the area given by 125%.Hence, we obtain the answer as 125% which is option (C).Note: The possibility of error in this question is using old length and breadth given by x and y to determine the new area and the new percentage change in area. Always go for using new length l’ and new breadth b’ to determine the new area A’. More General Aptitude Interview Questions
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What is the increase in area when the sides of a rectangle are increased in length by 100 %? * 100% 300% 200% 400%?
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