Question

The length of a rectangle is 5 mm less than 4 times the width. If the perimeter is 75 mm, what is the length of the rectangle?

Answer 1

`\boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}`

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 )

`\boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}`

`\dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}`

`\dashrightarrow{ \sf{75 = 2(5w - 5)}}`

`\dashrightarrow{ \sf{75 = 10w - 10}}`

`\dashrightarrow{ \sf{10w - 10 = 75}}`

`\dashrightarrow{ \sf{10w = 75 + 10}}`

`\dashrightarrow{ \sf{10w = 85}}`

`\dashrightarrow{ \sf{ (10w)/(10) = (85)/(10) }}`

`\dashrightarrow{ \sf{w = 8 .5 \: mm}}`

Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle

`\sf{length \: of \: a \: rectangle = 4w - 5}`

`\dashrightarrow{ \sf{4 * 8.5 - 5}}`

`\dashrightarrow{ \sf{34 - 5}}`

`\dashrightarrow{ \sf{29 \: mm}}`

Length of a rectangle = 29 mm

Hope I helped!

Best regards! :D