Question

The length of a rectangle is one foot more than twice it’s width. if the area of the rectangle is 300 ft.² find the dimensions of the rectangle

Answer 1

Answer:

Length= 12  ft

Width= 25 ft

Step-by-step explanation:

We will use the area of the rectangle formula to solve this question. The formula is: $Area= length* width$

Let, the width of the rectangle is x, so the length is one foot more than twice it’s width, and is written as:  

width= 2x+1

Now the area of the rectangle is given as:

300 $ft^2$

So using the formula of the area of a rectangle, we get:

$Area= length* width\\\Rightarrow 300= x(2x+1)\\\Rightarrow 2x^2+x-300=0\\\Rightarrow x=\frac{-1 \pm \sqrt{1^2-4 \cdot \:2\left(-300\right)}}{2\cdot \:2}\\\Rightarrow x=12,\:x=-\frac{25}{2}$

But we will take only positive value of x, as length can't be negative.

So the dimensions of the rectangle are:

Length= 12  ft

Width= 25 ft