Maths-

General

Easy

Question

# What is the percentage change in the area of a rectangle obtained by decreasing its length and increasing its breadth by 5%?

Hint:

### i. Area of a rectangle = length × breadth

ii. % change in a given quantity = (Difference between the 2 quantities)/ Original Quantity

## The correct answer is: Final Answer:- ∴ There is a 0.25 % decrease in the Area of the new rectangle.

### Step-by-step solution:-

Let the length of the original rectangle be x units & Breadth be y units.

∴ As per the given conditions-

Length of the 2nd rectangle = original length - 5% = x - 5% of x = 95% of x = 95/100 x = 0.95x ...................... (Equation i)

Breadth of the 2nd rectangle = original breadth + 5% = y + 5% of y = 105% of y = 105/100 y = 1.05y ............. (Equation ii)

Area of the original rectangle = length × breadth

∴ Area of the original rectangle = x × y = xy ............................................................................................. (Equation iii)

Area of the second rectangle = length × breadth

∴ Area of the second rectangle = 0.95x × 1.05y = 0.9975 xy ...................................................................... (Equation iv)

% change in a given quantity = (Difference between the 2 quantities)/ Original Quantity.

∴ % change in the area of rectangles = Difference between the area of 2 rectangles / Area of the Original rectangle

∴ % change in the area of rectangles = (0.9975 xy - xy) / xy

∴ % change in the area of rectangles = -0.0025 xy / xy

∴ % change in the area of rectangles = -0.25 %

Final Answer:-

∴ There is a 0.25 % decrease in the Area of the new rectangle.

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