Question

The perimeters of two equilateral triangles 3
are in the ratio of 4:1. What is the ratio of
their areas?
(a) 2:1
(b) 4:1
(c) 16:1
Yo) 8:1​

Answer 1

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Answer : 16 : 1

Step-by-step explanation :

Area of equilateral Triangle = $\frac{\sqrt{3} }{2}(side)^2$

Let the side of first equilateral triangle = x

The side of second equilateral triangle = y

Let the area of 1st triangle be $\frac{\sqrt{3} }{2} x^2$

Area of 2nd triangle be $\frac{\sqrt{3} }{2} y^2$

Perimeter of equilateral triangle = 3*side

We need to find the ratio of area of two triangles.

Given Ratio of perimeter of two triangles = 4:1

$=>\frac{3x}{3y}=\frac{4}{1}[given]\\\\=>\frac{x}{y}=\frac{4}{1}$

Squaring on both sides , we get ,

$=>\frac{x^2}{y^2}=\frac{4^2}{1^2} \\\\=>\frac{x^2}{y^2}=\frac{16}{1}\\\\=>\frac{\frac{\sqrt{3} }{2} x^2}{\frac{\sqrt{3} }{2}y^2}=\frac{16}{1}$

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