a Consider the different measurements we take of rectangles. Determine if the equation looks more like area or perimeter.
B
b Consider the different measurements we take of rectangles. Determine if the equation looks more like area or perimeter.
A
a The area of the rectangle.
B
b The perimeter of the rectangle.
Practice makes perfect
a We are given a rectangle with sides that have polynomials for the length and width. We are asked what a particular expression represents. Let's look at the image more carefully.
Let's match the polynomials to those in the equation.
( 4x^2+2x-1)( 2x^2-x+3)
Now, if we call the long side the length, l = 4x^2+2x-1, and the short side width, w= 2x^2-x+3, we can rewrite our equation as follows.
l * w
This is the expression used for the area of a rectangle, A=l * w.
b Here, we can also rewrite the given expression using l = 4x^2+2x-1 and w= 2x^2-x+3.
2( 4x^2+2x-1) &+ 2( 2x^2-x+3)
&↓
2( l) &+ 2( w)
The expression 2l+2w is used to find the perimeter of a rectangle, P=2l+2w.
