If you have a wooden board that is 0.75 meters wide, how long should you cut it such that the golden ratio is observed? Used 1.618 as the value of Golden Ratio.
Answers
Answer:
For a rectangle, length/width=golden ratio
width=0.75
Let the length be x.
x/0.75=1.618
x=0.75*1.618=(3/4)*1.618=3*0.4045=1.2135.
Length of the rectangle is 1.2135 m.
The Length of the wooden board is 1.21 meters.
GIVEN
Width of the wooden board = 0.75 meters.
Golden ratio = 1.618.
TO FIND
Length of the wooden board.
SOLUTION
We can simply solve the above problem as follows;
We know that the golden ratio of a rectangle is the ratio of the sum of its dimension to its longer side.
Golden ratio = 1.618
Let the length of the rectangular wooden board be L meters.
We know that,
Golden ratio = L+b/L
Where,
L = length of the rectangle
b = Width of the rectangle
Putting the values in the above formula we get;
1.618 = L + 0.75/L
1.618 L = L + 0.75
Subtracting L in both RHS and LHS
1.618 L - L = 0.75
0.618L = 0.75
Dividing 0.618 in both LHS and RHS
L = 0.75/0.618
L = 1.21 m
Hence, The Length of the wooden board is 1.21 meters.
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