Question

the length of a rectangle is increased by 25pecentage while breadth is diminished by 30percentage what is the impact on area
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Answer 1

Answer:

The area will decrease is 12.5%

Explanation:

Let the length of original rectangle = a

Let the breath of original rectangle = b

Area of the rectangle = Length × Breath

Area of the rectangle = ab

As it is given in the question,

The length is increased by 25%

New length = (25/100) × a + a

New length = 1/4 × a + a

New length = (a/4) + a

New length = ( 4a + a )/4

New length = 5a/4

The breadth is decreased by 30%

New breath = b - (b × 30%)

New breath = b - ( b × 30/100 )

New breath = b - ( 3b/10 )

New breath = (10b - 3b)/10

New breath = 7b/10

The area of the new rectangle formed:

New length × New breah

⟹ 5a/4 × 7b/10

⟹ 35ab/40

⟹ 7ab/8

The difference in area of the first and second rectangle:

Original area - New Area

⟹ ab - ( 7ab/8 )

⟹ (8ab - 7ab/8 )

⟹ ab/8

The area has decreased as ( original area - New area ) is positive.

Percentage of Area decreased:

Change in area/Original area × 100

⟹ (ab/8)/ab × 100

⟹ ab/(8ab) × 100

⟹ 1/8 × 100

⟹ 12.5%

The area is decreased by 12.5%