The length of the shorter piece is 7 ft.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
According to the question
A 19-foot board is cut into two pieces.
i.e Two new pieces are made which have total length as 19 foot
The length of the shorter piece is 1 ft more than half the length of the longer piece.
i.e, Let Length of larger piece = x
Length of shorter piece = [tex]\frac{x}{2} +1[/tex]
Now,
Total length of new pieces = 19 foot
Length of larger piece + Length of shorter piece = 19 foot
By equation
x + [tex]\frac{x}{2} +1[/tex] = 19
[tex]\frac{3x}{2} + 1[/tex] = 19
[tex]\frac{3x}{2}[/tex] = 18
x = 12 ft
Length of shorter piece = [tex]\frac{x}{2} +1[/tex]
= [tex]\frac{12}{2} +1[/tex]
= 7 ft
Hence, the length of the shorter piece is 7 ft.
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