Question

FormulaPart 2 of 2The length of a rectangle is 2 meters longer than the width. If the area is 35 square meters, find the rectangle's dimensions. Round to the nearest tenth of a meter.The width is 5 meters.(Round to the nearest tenth.)The length is(Round to the nearest tenth.)

Answer 1

Width: 5 meters

Length: 7 meters

1) Given that, the area of a rectangle is the product between its length and height.

`A=lw`

2) Let's write two algebraic expressions for the length and the width according to the text:

`\begin{gathered} l=x+2 \\ w=x \end{gathered}`

And now, plug them into the Area, like this:

`\begin{gathered} A=lw \\ \\ 35=x(x+2) \\ \\ x(x+2)=35 \\ \\ x^2+2x-35=0 \end{gathered}`

Now, let's solve this quadratic equation to get the quantity of x:

`\begin{gathered} x=(-2\pm√(2^2-4\cdot\:1\cdot\left(-35\right)))/(2) \\ \\ x_1=(-2+12)/(2\cdot\:1)=(10)/(2)=5 \\ \\ x_2=(-2-12)/(2\cdot\:1)=(-14)/(2)=-7 \end{gathered}`

We cannot consider the negative measure for x, since measurements cannot be negative. So now, we can tell that the width is 5 and length is 5+2= 7