Question

The perimeter of a rectangular boo is 48 inches. How do you express the length of the book as a function of the width?

Answer 1

Hint: We know the formula of perimeter of a rectangle. That is \[p = 2\left( {l + w} \right)\] , where ‘p’ is the perimeter of a rectangle and ‘l’ is the length and ‘w’ is the width of the rectangle. They have given perimeter \[p = 48\] inches and substituting we will get the required answer.

Complete step-by-step answer:
We have,
 \[p = 2\left( {l + w} \right)\] .
Given, \[p = 48\]
Substituting we have,
 \[48 = 2\left( {l + w} \right)\]
Divide by 2 on both sides we have,
 \[\dfrac{{48}}{2} = \left( {l + w} \right)\]
 \[24 = \left( {l + w} \right)\]
Rearranging we have,
 \[l + w = 24\]
 \[l = 24 - w\]
Now they asked us to express the length of the book as a function of the width, so we replace \[l\] by \[f\left( w \right)\] .
 \[ \Rightarrow f\left( w \right) = 24 - w\] . This is the required answer.
Here the unit of the dimension is in inches.
So, the correct answer is “ \[ f\left( w \right) = 24 - w\] .”.

Note: If they ask us to express the width of the book as a function of the length for the same problem then we replace \[w\] by \[f\left( l \right)\] . Then the answer will be,
 \[ \Rightarrow f\left( l \right) = 24 - l\] .
In a rectangle we know that the opposite sides are parallel and equal to each other. Each interior angle is equal to 90 degrees. The sum of all the interior angles in a rectangle is equal to 360 degrees. We also know that the area of a rectangle is \[ab\] square units, where ‘a’ and ‘b’ are the sides of the rectangle.