Question

if the length of each side of a triangle is decreased by 20% th ️ what is the present decrease in the area of the​

Answer 1

Answer:

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

If side 'a' is decreased by 20%, new side = 0.8a or 4a/5 cm

Area of equilateral triangle with side 4a/5 = √3/4 × (4a/5)² = 4(√3a²)/5

⇒ Decrease in area = √3/4 × (a)² - 4(√3a²)/5 = 9(√3a²)/100

⇒ Percentage decrease = [9(√3a²)/100]/[√3/4 × (a)²] × 100

∴ Percentage decrease in area = 36%.

Answer 2

Answer:

Let the hight and base of the triangle is h and b respectively.

So, area = (1/2 )(b×h)=bh/2

h decreased by 20% becomes h-(h×20)/100 =h-(h/5)= 4h/5

b increased by 20% becomes b+(b/5)=6b/5

New area =(1/2)(6b/5)(4h/5)

=24bh/50

Area decreased by (bh/2)-(24bh/50) =(25bh-24bh)/50 =bh/50

%of decrease = {(bh/50)×100}/bh/2= 2bh/bh/2

=4bh/bh =4%

Area decreased by 4%

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