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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: How much is the area of equilateral triangle decreased, if the sides of an equilateral triangle are decreased by 20%? Quantity B: 40%

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: How much is the area of equilateral triangle decreased, if the sides of an equilateral triangle are decreased by 20%? Quantity B: 40% Correct Answer <span style=" line-height: 107%; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Quantity A &lt; Quantity B</span>

Quantity A:

Area of an equilateral triangle = (√3/4) × a2

Where ‘a’ represents side of an equilateral triangle

Percentage of change in area of equilateral triangle = (change in area/ original value of area) × 100

Let the side of an equilateral triangle be 100 units

Area of an equilateral triangle = (√3/4) × (100)2

⇒ 2500√3 square units

According to question,

Sides of an equilateral triangle decreased by 20%

∴ New side of an equilateral triangle is 80

Now, area of equilateral triangle is (√3/4) × (80)2

⇒ 1600√3 square units

Change in area = 2500√3 – 1600√3

⇒ Change in area = 900√3 square units

∴ Percentage of change in area of equilateral triangle = (900√3/2500√3) × 100 = 36%

Quantity B: 40%

∴ Quantity A < Quantity B

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