Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}[/tex]
Step-by-step explanation:
Let the width of a rectangle be 'w'
Length of a rectangle be 4w - 5
Perimeter of a rectangle = 75 mm
First, finding the width of the rectangle ( w )
[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 2(5w - 5)}}[/tex]
[tex] \dashrightarrow{ \sf{75 = 10w - 10}}[/tex]
[tex] \dashrightarrow{ \sf{10w - 10 = 75}}[/tex]
[tex] \dashrightarrow{ \sf{10w = 75 + 10}}[/tex]
[tex] \dashrightarrow{ \sf{10w = 85}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}[/tex]
[tex] \dashrightarrow{ \sf{w = 8 .5 \: mm}}[/tex]
Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle
[tex] \sf{length \: of \: a \: rectangle = 4w - 5}[/tex]
[tex] \dashrightarrow{ \sf{4 \times 8.5 - 5}}[/tex]
[tex] \dashrightarrow{ \sf{34 - 5}}[/tex]
[tex] \dashrightarrow{ \sf{29 \: mm}}[/tex]
Length of a rectangle = 29 mm
Hope I helped!
Best regards! :D
