00:01
Let's determine the length and width of the electronic sign, which is in the shape of a rectangle.
00:06
So here i have drawn the rectangle which represents the electronic sign.
00:11
And l represents the length of the electronic sign and w is the width of the electronic sign.
00:16
We are told that the perimeter is 44 feet and the area of the electric sign is 96 feet square.
00:24
So we use this to information to determine the length and width.
00:27
So first is consider the perimeter information.
00:31
Perimeter is the total distance covered of the outer boundary.
00:36
So in a rectangle, the opposite side lengths are the same.
00:39
So if l is the length, the opposite side length is also l.
00:44
And if w is the width of the rectangle, the opposite side length is also w.
00:49
And so the perimeter is, so we have to measure the total distance.
00:53
That is l plus w plus l plus l plus w and so basically this equals l plus l is 2l plus w plus w is 2 w and this is given as 44 feet so now we have represented this in equation let's focus this equation 2 l plus 2 w equals 44 i'm going to factor 2 from the right side expression.
01:21
When i do the 2, i will be getting 2 times of l plus w and this equals 44.
01:28
Let's divide both sides by 2.
01:31
So this will cancel out 1 times.
01:34
And on the left we get l plus w equals 44 divided by 2 is 22.
01:40
So we have simplified this perimeter information to l plus w equals 22.
01:47
Let's say this is equation number one.
01:50
Now let's use the other information that is area is 96b squared.
01:55
We know the area of a rectangle is the product of its length and width.
01:59
So length and width is a product and this is given as 96.
02:04
So let's consider this as equation two.
02:07
Now we have to solve these two equations, one and two for l and w.
02:12
I'm going to use the substitution method.
02:15
Consider this l plus w equals 22.
02:19
From this let's determine w by subtracting l from both sides.
02:24
And when we do that, we get w equals 22 minus l.
02:28
So basically we are going to substitute w into this equation.
02:34
When you do that, we get l times of 22 minus l.
02:39
And this equals 96.
02:42
Let's do the distribution.
02:45
We distribute like this.
02:47
L times 22 is 22l minus l times negative l is negative l squared.
02:53
And this equals the 96...