prove that the area of the equilateral triangle described on side of a square is half of area of the equilateral triangle described on its diagonal
q17 q18 q19
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it's in the picture
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17. draw a square mark it as ABCD
sol:
let ABCD be a square where AC is a digonal.
to prove=ar.of eq.triangle in AD= 1/2 ar of eq.triangle on AC
proof:
since, ABCD is a square
angle D = 90 degree
in triangle ADC,
AC^2=AD^2+DC^2
=>AC^2= AD^2+ AD^2. (since AD=DC)
=> AC^2= 2AD^2
=>1/2AC^2=AD^2
=>1/2* root3/4AC^2= root3/4AD^2
( multiplying root3/4 both sides)
so,
1/2 ar.of eq.triangle on AC = ar of eq.triangle on AD.
sol:
let ABCD be a square where AC is a digonal.
to prove=ar.of eq.triangle in AD= 1/2 ar of eq.triangle on AC
proof:
since, ABCD is a square
angle D = 90 degree
in triangle ADC,
AC^2=AD^2+DC^2
=>AC^2= AD^2+ AD^2. (since AD=DC)
=> AC^2= 2AD^2
=>1/2AC^2=AD^2
=>1/2* root3/4AC^2= root3/4AD^2
( multiplying root3/4 both sides)
so,
1/2 ar.of eq.triangle on AC = ar of eq.triangle on AD.
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