00:01
All right, on this problem, we are told that we have a rectangle.
00:03
The parameter of the rectangle is 28.
00:05
So if we've got sides of x and y, then that means 2x plus 2y is equal to 28.
00:16
Divide everything by 2 there.
00:17
So that tells us x plus y is equal to 14.
00:23
Perimeter just means add up all the sides.
00:25
So that's the first equation we're going to get from this.
00:27
X plus y is 14.
00:29
Now we know the diagonal is 10.
00:32
So with pythagorean theorem, that tells us that x squared.
00:35
Plus y squared is equal to 10 squared, which is 100.
00:41
So x squared plus y squared is equal 100 because rectangles have angles of 90 degrees, and so we can use pythagorean theorem.
00:48
So now we have this system to solve.
00:52
Now this top equation, when you take the x over, that tells us y is 14 minus x.
00:58
And so we're going to substitute that down in here for y.
01:02
So we have x squared plus 14 minus x squared.
01:09
Equals 100, square 14 minus x, so you have to multiply it by itself and foil it.
01:18
So that would be 196 minus 28x plus x squared.
01:26
And i'll leave that to you to verify that that's what it is, but you multiply it by itself and foil it out...