Question

রফিকদের আয়তক্ষেত্রাকার মেঝের দৈর্ঘ্য 2 মিটার এবং প্রস্থ 3 মিটার বৃদ্ধি করলে ক্ষেত্রফল 75 বর্গমিটার বৃদ্ধি পায়। কিন্তু দৈর্ঘ্য 2 মিটার হ্রাস এবং প্রস্থ 3 মিটার বৃদ্ধি করলে ক্ষেত্রফল 15 বর্গমিটার বৃদ্ধি পায়। সহসমীকরণ গঠন করে রফিকদের মেঝের দৈর্ঘ্য ও প্রস্থ নির্ণয় করি।​

Answer 1

The length and width are 15 cm and 12 cm respectively.

• An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
• Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Now, according to the given information, it is given that,

Increasing the length of Rafiq's rectangular floor by 2 meters and width by 3 meters increases the area by 75 square meters.

Let the length be x and the width be y.

Then, area of the rectangular floor = xy.

Now, (x+2) × (y+3) = xy + 75

Or, xy +3x +2y + 6 = xy + 75

Or, 3x +2y = 69....(1)

Again, we are given that, reducing the length by 2 meters and increasing the width by 3 meters increases the area by 15 square meters.

That is, (x-2) × (y+3) = xy + 15

Or, xy + 3x - 2y -6 = xy + 15

Or,  3x - 2y = 21....(2)

#Adding equations 1 and 2, we get,

6x = 90

Or, x = 15 cm.

Then, y = $\frac{69-45}{2} = 12 cm.$

Hence, the length and width are 15 cm and 12 cm respectively.

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