[SOUND]. Lets look at word problems, that involve

area and perimeter. [SOUND].

For example, the length of a rectangle is five times its width.

If the area of the rectangle is 405 square feet, find its perimeter.Okay, so

lets let l = length of the rectangle, and w = the width.

That is, this is l and this is w. Now we're told that the length, is 5

times its width. Which means then that l the length, is

equal to 5 times the width of 5 w. But we're also told that the area of the

rectangle is 405 square feet. And remember that the area.

Of a rectangle, is the length * width. Which means that the length * width = 405

square feet. Now we know that l = 5w, so lets replace

l here with 5 * w. Which gives us, (5w) w = 405.

Or, 5w^2 = 405. And then, dividing both sides by 5 gives

us w ^ 2 is equal to 81. Which means w is equal to plus or minus

the square root 81. But since w is the width of this

rectangle here, were going to choose the positive.

So w is positive square root 81, or positive 9.

And then we can plug this back in here, to give us what l is equal to.

That is, l = 5 * 9 Or 41. So let's write that up here.

l, the length of the rectangle is 45 feet.

And w, the width, is 9 feet. However, this isn't what we're asked to

find, is it? We're asked to find its perimeter remember the perimeter of a

rectangle is 2 x the length + 2 x the width.

So plugging in the values we just found for l and w, we'll be able to find this

perimeter. Namely, p is = to 2 x 45, + 2 x 9 or p =

To 90 + 18 = 108. So therefore our asnwer is 108 feet.

Alright lets look at 1 more. The length of a rectangle is 4

centimeters longer, than its width. If the perimeter of the rectangle is 48

cm, find it's area. Again, let's say l = the length of the

rectangle, and w = to its width. Now we're told that the length.

Is 4 cm longer than it's width. Therefore l = w + 4.

But now in this example, we're given what the perimiter is equal to.

It's 48 cm, and we want to find the area. Again we can use the formula that the

perimeter of a rectangle is 2 times its length plus 2 times its width, which we

are given is equal to 48, which means 2 times l plus 2 times w has to be equal to

48. And now we can replace l here with w + 4,

which gives us 2 times, · be careful, it's the whole quantity of (w+4). Or 2w +

8 + 2w = 48 or 4w + 8 = 48 and then subtracting 8 from both sides gives us 4w

= 48 - 8 or 4w = 40. And then dividing both sides by 4, gives

us that w = 10. And then we can plug this value back into

this equation, to find l. Namely, l is = 10 + 4 or 14.

So, let's write that up here, l = 14 cm and w = 10 cm.