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The length of a rectangle is the sum of the width and one. The area direct angle 72 units. What’s the length, in units, of the rectangle

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Answer:

The length of the rectangle is of 9 units.

Explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:


ax^(2) + bx + c, a\\eq0.

This polynomial has roots
x_(1), x_(2) such that
ax^(2) + bx + c = a(x - x_(1))*(x - x_(2)), given by the following formulas:


x_(1) = (-b + √(\bigtriangleup))/(2*a)


x_(2) = (-b - √(\bigtriangleup))/(2*a)


\bigtriangleup = b^(2) - 4ac

Area of a rectangle:

A rectangle has width
w and length
l. The area is the multiplication of these measures, that is:


A = wl

The length of a rectangle is the sum of the width and one.

This means that
l = w+1, or
w = l - 1

The area direct angle 72 units. What’s the length, in units, of the rectangle

We want to find the length. So


wl = 72


(l-1)l = 72


l^2 - l - 72 = 0

Quadratic equation with
a = 1, b = -1, c = -72. So


\bigtriangleup = (-1)^(2) - 4(1)(-72) = 289


l_(1) = (-(-1) + √(289))/(2*(1)) = 9


l_(2) = (-(-1) - √(289))/(2*(1)) = -8

Since the length is a positive measure, the length of the rectangle is of 9 units.

User Mike Wade
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