the perimeter of a rectangle is 124 cm. the length is six more than three times the width. what are the dimensions of the rectan
gle?
2 answers:
Our first task in this problem is to set up variables that represent length and width.
<u>Let's first identify our values:</u>
X → Width
3x + 6 → Length
Before moving on, it's always a great idea to draw a picture of the rectangle to visualize what's going on. I will provide a picture.
Now, we can use the first sentence of the problem to set up our equation.
The perimeter of a rectangle is the distance around the outside of the figure. If our perimeter is 124 cm, we can set up an equation to represent this.
<h3>x + x + 3x + 6 + 3x + 6 = 124cm.</h3><h3 /><h3>If we simplify on the left side we will get </h3><h3>8x + 12 = 124</h3><h3> -12 -12</h3><h3 /><h2>8x = 112</h2><h2>÷8 ÷8</h2><h2 /><h2>X = 14</h2><h2 /><h2>Width = 11 cm</h2><h2>Length = 48 cm</h2>
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( + 4)(
- 4)
To solve this question you must FOIL (First, Outside, Inside, Last) like so
First:
(x^2 + 4)(x^2 - 4)
x^2 * x^2
x^4
Outside:
(x^2 + 4)(x^2 - 4)
x^2 * -4
-4x^2
Inside:
(x^2 + 4)(x^2 - 4)
4 * x^2
4x^2
Last:
(x^2 + 4)(x^2 - 4)
4 * -4
-16
Now combine all the products of the FOIL together like so...
x^4 - 4x^2 +4x^2 - 16
Combine like terms:
x^4 - 4x^2 +4x^2 - 16
- 4x^2 +4x^2 = 0
x^4 - 16 <<<This is your answer
Hope this helped!
~Just a girl in love with Shawn Mendes