প্রশ্নে বলা হচ্ছে, একটি আয়তক্ষেত্রের পরিসীমা 104 ইঞ্চি। এর প্রস্থ দৈর্ঘের 3 গুণ অপেক্ষা 6 ইঞ্চি কম হলে প্রস্থ কত?

ধরি, দৈর্ঘ্য x ইঞ্চি

∴ প্রস্থ = (3x - 6) ইঞ্চি।

প্রশ্নমতে, 2(দৈর্ঘ্য + প্রস্থ) = 104

⇒ 2(x + 3x - 6) = 104

⇒ 4x - 6 = 52

⇒ 4x = 58

∴ $x=\frac{58}{4}$

= 14.5

∴ নির্ণেয় প্রস্থ = 3x - 6 = 3 $\times$ 14.5 - 6 = 43.5 - 6 = 37.5 ইঞ্চি।

Let L represent the length of the rectangle in inches, and let W represent the width of the rectangle in inches.

According to the problem, the width is 6 inches less than 3 times the length, so we can write this as an equation:

W = 3L - 6

The perimeter of a rectangle is given by the formula:

Perimeter = 2(L + W)

In this case, the perimeter is 104 inches, so we can write:

104 = 2(L + W)

Now, substitute the expression for W from the first equation into the perimeter equation:

104 = 2(L + (3L - 6))

Simplify the equation:

104 = 2(4L - 6)

Now, distribute the 2 on the right side of the equation:

104 = 8L - 12

Add 12 to both sides of the equation to isolate the 8L term:

104 + 12 = 8L

116 = 8L

Now, divide both sides by 8 to find the value of L:

L = 116 / 8 L = 14.5

So, the length of the rectangle is 14.5 inches.

Now, use the first equation to find the width:

W = 3L - 6 W = 3(14.5) - 6 W = 43.5 - 6 W = 37.5

So, the width of the rectangle is 37.5 inches.