# The length of the rectangle is 5 meters longer than the width. What width should the rectangle

The length of the rectangle is 5 meters longer than the width. What width should the rectangle have so that its area is more than 36 m ^ 2.

Let us denote the width of the rectangle by x m and compose the inequality according to the problem statement.

x * (x + 5)> 36;

Move the free term to the left side of the inequality, expand the brackets, equate the quadratic trinomial to zero and find the roots of the quadratic equation.

x ^ 2 + 5x – 36> 0.

x ^ 2 + 5x – 36 = 0;
D = 5 * 5 + 4 * 36 = 25 + 144 = 169 = 13 ^ 2.

x1 = (- 5 + 13) / 2 = 8/2 = 4;
x2 = (- 5 – 13) / 2 = – 18/2 = – 9.

(x – 4) (x + 9)> 0.

x – 4> 0;
x + 9> 0.

x> 4;
x> – 9.

Answer: the width of the rectangle must be more than 4 m.

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