Draw an equilateral triangle on anyone side of a square. Also draw an equilateral triangle on the diagonal of the square. Calculate the area of both the triangles using Heron’s formula only. Compare their areas and write as a ratio.
Answers
Answer:
Their area are same and the area = √3y⁴/16
1 : 1
Step-by-step explanation:
side of the square=x
side of equilateral triangle=y (where y=x as we have drawn a equilateral triangle on the square side because of which x=y)
s=(y+y+y)/2
3y/2
Area= √3y/2((3y/2)-y)((3y/2)-y)((3y/2)-y)
= √3y/2((3y-2y)/2)((3y-2y)/2)((3y-2y)/2)
= √3y/2*y/2*y/2*y/2
= √3y/2*(y/2)³ = √3y/2*y³/8
= √3y⁴/16
The second triangle we have to draw in the diagonal of the square will also have same area as the first triangle because as we know a single diagonal will divide the square in two equilateral triangle in so, if we draw a square and make a single diagonal we will observe that the base is the side of the square and it is an equilateral triangle so, hence,
Area of 1 triangle = Area of 2 triangle
Their Ratio= (√3y⁴/16) / (√3y⁴/16)
= 1 : 1
Answer:
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