The diagonal of a square is twice the side of an eqilateral triangle. Find the ratio of the area of the square to the area of the triangle.
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Hello Prasad!
Side of square= a
Diagonal= √2*a
Side of equilateral triangle= a/√2
Area of square= a 2
Area of equilateral triangle= (√3/4)*( a/√2) 2 = (√3/8)* a 2
Ratio of area of square to triangle = a 2 /(√3/8)* a 2 = 8/√3
Hope this helped:)
Hi Prasad!
Let side of equilateral triangle =x
Length of diagonal of square = 2x
Area of square= 1/2 (diagonal 1 )(diagonal 2)
Area of square = 1/2 (2x)²
Area of square = 1/2 (4x²)
Area of square= 2x²
Find ratio of triangle to square:
triangle : square = √3/4 x² : 2x²
Divide both sides by x²:
triangle : square = √3/4 : 2
Multiply both sides by 4:
triangle : square = √3 : 8
Hope it helped to clear your delimma.
Hello!
Let the diagonal of sq. be '2x' & side of equilateral be 'x' uts.
The side of sq will be (x√2) uts. (By using Pythagoras theorem)
(Side)²+(side)² = (2x)²
Therefore side of sq. Is x√2
Area of square = a² = ( x√2 )² = 2x²
Area of equilateral = √3/4 a² = √3/4 (x²)
Ratio of area of square: area of equilateral triangle = (2x²) ÷ (√3/4 x²) = 8 : √3
i hope this helps.
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