Question

The length of a rectangle is 5m less than three times the width, and the area of the rectangle is 50m^(2). Find the dimensions of the rectangle

Answer 1

Answer:

The width is 5m and the length is 10m.

Step-by-step explanation:

Rectangle:

Has two dimensions: Width(w) and length(l).

It's area is:

$A = w*l$

The length of a rectangle is 5m less than three times the width

This means that $l = 3w - 5$

The area of the rectangle is 50m^(2)

This means that $A = 50$. So

$A = w*l$

$50 = w*(3w - 5)$

$3w^{2} - 5w - 50 = 0$

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:

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

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

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

In this question:

$3w^{2} - 5w - 50 = 0$

So

$a = 3, b = -5, c = -50$

$\bigtriangleup = (-5)^{2} - 4*3*(-50) = 625$

$w_{1} = \frac{-(-5) + \sqrt{625}}{2*3} = 5$

$w_{2} = \frac{-(-5) - \sqrt{625}}{2*3} = -3.33$

Dimension must be positive result, so

The width is 5m(in meters because the area is in square meters).

Length:

$l = 3w - 5 = 3*5 - 5 = 10$

The length is 10 meters