Question

A piece of recangular paper of size 5 m $\times$ x m is cut from each side by 2 m to make a smaller rectangle. Determine
the maximum breadth of the smaller rectangle if it's perimeter is maximum 68 m.

• A. 35
• B. 38
• C. 4
• D. 8

Answer 1

The correct option is B 38

Given,
Length of paper before cutting $=5$ m
Breadth of paper before cutting $=x$ m
Since, paper is cut from both the sides by 2 m, hence the net length cut is $2+2=4$ m

Length of paper after cutting $=5-4=1$ m

Breadth of paper after cutting $=X-4$ m

As we know,
Perimeter of a rectangle = 2(Length + breadth)
Given, Perimeter of smaller rectangle$\le 68$ m
$2(1+x-4)\le 68$
Transfer 2 to the R.H.S
$1+x-4\le 39$ ($\because \frac{68}{2}=39$)
$x-3\le 39$
Add 3 both the sides
$x-3+3\le 39+3$
$x\le 42$ m
Breadth of paper after cutting $=x-4$ m
Breadth of paper after cutting $\le 42-4$ m
Breadth of paper after cutting $\le 38$ m
A closed circle at $38$ and the red line goes to the left, indicating that $x$ is less than or equal to $38$

Hence, the maximum possible value for the breadth of the smaller rectangle is 38 m
Hence, option(b) is correct.