Question

A wire is in the form of a square of side 16cm. It is bent to make a rectangle of width equals 10cm. Find the length of the rectangle. Find which one has max area.

Answer 1

Hint: Put focus on the line “square is bent to make a rectangle” it means both square and rectangle will have same perimeter, now using this line in mathematical format
Perimeter of square is \[4a\] (here a is the side length)
Perimeter of rectangle is\[2(l+b)\], (here l is the length and b are the width)
Now in question we are given values of a and b. so we just equate these both and find the value of l.

Complete step by step answer:
Given a wire is in the form of a square of side 16cm. then it is bent to make a rectangle of width equals 10cm and we have to find the length of the rectangle and which one has max area.
So as looking at the question carefully there is a line “square is bent to make a rectangle”
This means that both square and rectangle will have same perimeter, now we can write this mathematical format and as we know the basic perimeter formulas
Perimeter of square is \[4a\] (here a is the side length)
Perimeter of rectangle is\[2(l+b)\],(here l is the length and b are the width)
We have to equate these perimeters and write expression as \[4a=2(l+b)\]
In the question we are given the value of a (side length of square) equals to 16 cm and value of b (width of rectangle) equals to 10cm
So, putting these values in equation \[4a=2(l+b)\]
We get expression as \[4\times 16=2(l+10)\] solving it we get \[64=2(l+10)\] further solving gives
\[32=(l+10)\] and finally, \[l=22\]
So, length of rectangle would be 22cm
Now we have to find areas of both rectangle and square and compare them
Area of square = \[{{a}^{2}}\] and Area of rectangle = \[(l\times b)\]
Putting the values, we get
Area of square = \[{{16}^{2}}=256\] and
Area of rectangle = \[(22\times 10)=220\]

So, we can see very clearly that area of square is maximum.

Note: Most of the students made mistakes while taking the perimeter of the rectangle as only (L+b) and forgets to multiply it with 2. Above method is also applicable if square wire changes to any other shape; we just need to know the perimeter and area of that shape.