Step-by-step explanation: Our first task in this problem is to setup variables representing <em>length</em> and <em>width</em> and we do that by using the second sentence.
<em><u>The length is twice the width</u></em>
So if we call our width <em>x</em>, that means that our length is 2 times <em>x</em> or 2x
Width of the rectangle ⇒ <em>x</em>
Length of the rectangle ⇒ <em>2x</em>
Before moving on, go ahead and draw a picture of your
rectangle so that you can visualize what's going on.
I have done this for you below.
We label our widths <em>x</em> and our lengths <em>2x</em>.
Now we can use the first sentence to setup our equation.
The perimeter of a rectangle is the distance
around the outside of the figure.
So if our perimeter is 60, that means that x + x + 2x + 2x = 60.
Simplifying by combining like terms, we get 6x = 60.
Now dividing both sides by 6, we find that <em>x = 10</em>.
Since <em>x</em> represents width, our width is 10.
Our length therefore with be <em>2(10)</em> or 20.
So our width is 10 and our length is 20.
Answer:
Step-by-step explanation:
When working with surds we need to take note of the roots present there.
To expand this equation we can do it the following way noting that √3 X √3 = 3
<em></em>
<em>Expanding (1-√3)(⅓+√3)</em>
1 X 1/3 = 1/3
1 X √3 = √3
-√3 X 1/3 =-√3/3
√3 X √3 = 3
hence, expanding the equation, we have
1/3 + √3 -√3/3 + 3
We can simply group the like terms and add them up.
[1/3 +3] +[√3-√3/3]
10/3 +
=
Step-by-step explanation:
