Question

The side of a traingle are in ap and its area is 3/5*area of an equilateral triangle of same perimeter then ratio of the sides

Answer 1

Step-by-step explanation:

Let the sides of a triangle are (a-d) , a and (a+d) units.

s=(a-d+a+a+d)/2=3a/2

Area of the triangle=√[3a/2(3a/2-a+d)(3a/2-a).(3a/2-a-d)].

= √[3a/2.(a/2+d).a/2.(a/2-d)]

= a/4.√[3.(a^2-4d^2) units ^2

Perimeter of this ∆=a-d+a+a+d=3a

Length of each side of an equilateral triangle= 3a/3= a

Area of the equilateral triangle=(√3.a^2)/4. , Acordingly:-

a/4.√[3.(a^2-4d^2) =3/5 of (√3.a^2)/4

√(a^2-4d^2). = (3/5).a

Squaring both sides

a^2-4d^2=9a^2/25

or. 25a^2–100d^2=9a^2

or. 16a^2=100d^2

or. 4a^2=25d^2

or. d=+/-2a/5 (leaving -ve value)

d= 2a/5

Length of 1st side =a-d=a-2a/5. = 3a/5

Answer 2

Answer:

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