width = 19 cm
Length = 39cm
Step-by-step explanation:
Perimter of the rectangle = 116cm
length = 1cm more than twice its width
length = 1cm + 2(width)
Perimeter of a rectangle = 2(length + width)
= 2(length) + 2(width)
Perimeter of the rectangle = 2[1cm + 2(width)] + 2(width)
Perimeter of the rectangle = 2cm + 4(width) + 2(width)
116 = 2 + 6(width)
subtract 2 from both sides:
116 - 2 = 2-2 + 6(width)
114 = 6(width)
divide both sides by 6:
114/6 = 6(width)/6
width = 19 cm
Length = 1cm + 2(width)
Length = 1cm + 2(19cm) = 1cm + 38cm
Length = 39cm