A few days ago
Weird word problem function?
I normaly dont this but im stumpted , i have been working for a few hours now on these and i jsut cant get this one. any help would be greatly appricated , im not just looking for an answer tho, an explination would be awesome too.
(1 pt) Given a rectangle whose length is always 2 times of its width. Express the area A of this rectangle in a function of its perimeter x.
Step1: Assume that the length and width of the rectangle are L and w respectively. Then L can be expressed in terms of w, i.e.
L=2*w
and the peremiter can be written as
x=2*w+2*L=2*w +2*2*w.
Step2: Express w and L as functions of x:
W=
L=
Step3: Express area A=w*l as a function of x:
A= .
Top 1 Answers
A few days ago
Favorite Answer
You don’t really need to use a separate letter for the length. That seems to add confusion. It gives you more equations, meaning you have to do more elimination.
The width of the rectangle is w, and its length is 2w.
If a is the area and x the perimeter, then:
a = 2w*w
a = 2w^2 ………(1)
x = 2(w + 2w)
x = 2*3w
x = 6w ………(2)
From (2):
w = x / 6
Substituting this value for w in (1):
a = 2(x / 6)^2
a = 2x^2 / 36
a = x^2 / 18.
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