Question

A rectangle has a length of 23 feet less than 3 times it’s width. If the area of the rectangle is 2870 square feet, find the length of the rectangle. Feet?

Answer 1

Okay, here we have this:

We obtain the following from the statement:

Width=x

Lenght=3*Width-23=3x-23

`\begin{gathered} Area=Width\cdot Lenght \\ 2870=x\mleft(3x-23\mright) \\ 3x^2-23x=2870 \\ 3x^2-23x-2870=0 \\ x_(1,\: 2)=(-\left(-23\right)\pm√(\left(-23\right)^2-4\cdot\:3\left(-2870\right)))/(2\cdot\:3) \\ x_(1,\: 2)=(-\left(-23\right)\pm\:187)/(2\cdot\:3) \\ x_1=(-\left(-23\right)+187)/(2\cdot\:3),\: x_2=(-\left(-23\right)-187)/(2\cdot\:3) \\ x_1=35,x_2=-(82)/(3) \end{gathered}`

And, as the measure cannot be negative we are left alone with x=35.

This mean that the width is 35feet. Now, let's replace to find the lenght:

Lenght=3*Width-23

Lenght=3*35-23

Lenght=105-23

Lenght=82 feet.