Question

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

Answer 1

Answer:

The length of the rectangle is of 9 units.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$.

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:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

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

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

$l_{1} = \frac{-(-1) + \sqrt{289}}{2*(1)} = 9$

$l_{2} = \frac{-(-1) - \sqrt{289}}{2*(1)} = -8$

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