If the perimeter of square & equilateral triangle is same. If the side of equilateral triangle is 8 cm. Find the area of the square.
Answer with explanation
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If the perimeter of square & equilateral triangle is same. If the side of equilateral triangle is 8 cm. Find the area of the square.
Answer with explanation
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Given,
The side of the equilateral triangle is [tex]8 cm[/tex]
The perimeter of the square and equilateral triangle is the same.
To find,
Area of the square
Solution,
The perimeter of square= 4 × side
Let us substitute the word side with [tex]s[/tex]
Perimeter = [tex]4s[/tex]
The perimeter of an equilateral triangle = 3 × side
Let us substitute sides with [tex]a[/tex]
Perimeter = [tex]3a[/tex]
The Perimeter of square = Perimeter of triangle
[tex]4s = 3a[/tex]
[tex]s =[/tex] [tex]\frac{3}{4}[/tex] [tex]a[/tex]
The side of the triangle is given as [tex]8cm[/tex]
[tex]s =[/tex] [tex]\frac{3}{4}[/tex] × 8
[tex]= 6 cm[/tex]
The side of the square is [tex]6cm[/tex]
Area of the square = side × side
[tex]= 6[/tex] × [tex]6[/tex]
[tex]36 cm^{2}[/tex]
Therefore the area of the square is [tex]36cm^{2}[/tex]