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

Answer:

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

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 )

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

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

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

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

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

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

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

$\dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}$

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

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

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

$\dashrightarrow{ \sf{4 \times 8.5 - 5}}$

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

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

Length of a rectangle = 29 mm

Hope I helped!

Best regards! :D