Find the variables and lengths of the sides of this kite.
{top left is y-4, top right is x+5, bottom left is 2x+5, and bottom right is x+12}
Thank you (:
Assuming symmetry for a kite,
y-4 = x+5
2x+5 = x+12
from the second equation,
x=7
plugging that into the first equation,
y=16
so, the short sides are 12, the long sides are 19
Check for typos. This is the second problem you've posted that doesn't follow the usual pattern of having n equations in n variables.
When you plug in the numbers into the equations it equals to short sides = 12 long sides = 19
wait how do you have shorter sides being 12 and 19 for the longer sides if you have x=7 and y=16 (Steve)
Oh, a kite! The kind that flies in the sky, not the bird kind, right? Alright, let's see what we got here.
The variables in this kite are:
- x: The mysterious, elusive variable that makes appearances in all sorts of math problems.
- y: Another sneaky variable that likes to hide in equations.
Now, let's talk about those side lengths. Here's what we have:
- Top left to top right: (x + 5) - (y - 4) = x - y + 9 (Didn't expect some algebra, did ya?)
- Bottom left to bottom right: (x + 12) - (2x + 5) = -x + 7
But wait, there's more! We can simplify that second equation a bit:
- Bottom left to bottom right: -x + 7
There you go! The variables and lengths of the sides of this kite, in all their mysterious and simplified glory. Have a good one!
To find the variables and lengths of the sides of the kite, we first need to understand the properties of a kite. In a kite, the two pairs of adjacent sides are of equal length.
Let's label the sides of the kite as follows:
- Top side: y-4
- Bottom side: 2x+5
- Left side: y-4
- Right side: x+12
From the given information, we can set up equations to find the values of x and y.
Since opposite sides of a kite are equal, we can equate the top and bottom sides:
y-4 = 2x+5
Similarly, we can equate the left and right sides:
y-4 = x+12
We now have a system of two equations with two variables. Let's solve it:
1) y-4 = 2x+5
Rearrange the equation: 2x-y = -9
Multiply both sides by -1 for easier solving: -2x+y = 9 (Equation 1)
2) y-4 = x+12
Rearrange the equation: x-y = -16 (Equation 2)
We can solve this system of equations either by substitution or elimination method:
Using substitution method:
From Equation 2, we can express x in terms of y: x = y-16
Now substitute this value of x in Equation 1:
-2(y-16) + y = 9
Solve for y:
-2y + 32 + y = 9
-y = 9 - 32
-y = -23
y = 23
Now that we have the value of y, substitute it back into Equation 2 to find x:
x - 23 = -16
x = -16 + 23
x = 7
Therefore, the variables for the kite are x = 7 and y = 23.
To find the lengths of the sides, substitute the values of x and y into the expressions for each side:
Top side: y-4 = 23-4 = 19 units
Bottom side: 2x+5 = 2(7)+5 = 14+5 = 19 units
Left side: y-4 = 23-4 = 19 units
Right side: x+12 = 7+12 = 19 units
So, all the sides of the kite have a length of 19 units.