Question

Find the possible length and breadth of the rectangle whose area is x

2 + 9x + 20.

Answer 1

11 cm.

• 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.
• 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.

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

The area of a rectangle is equal to 2 + 9x + 20.

Let the length and breadth be equal, say, x.

Then, we have, $x^{2} = 2+9x+20$

Or, $x^{2} -9x-22=0$

Or, $x^{2} -11x+2x-22=0$

Or, (x+2)(x-11) = 0.

Then, x = 11.

Hence, the length and breadth of the rectangle is 11 cm and 11 cm respectively.

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