One side of a kite is 4 cm less than four times the length of another side. The perimeter of the kite is 59 cm. Find the lengths of the sides of the kite.

A kite is a quadrilateral whose diagonals intersect at 90°.

One of the diagonals is an axis of symmetry that divides the figure into two congruent triangles.
So if "One side of a kite is 4 cm less than four times the length of another side (x). ", we have
(4x-4) + x = 59/2
5x = 33.5
x=6.7 cm
The other side = 4x-4=22.8 cm

To solve this problem, let's set up equations based on the given information.

Let's assume the length of one side of the kite is x cm.
According to the problem, one side of the kite is 4 cm less than four times the length of another side. This can be written as:
x = 4(Another side length) - 4

The perimeter of the kite is the sum of the lengths of all four sides. In this case, it is given as 59 cm. So we can write:
x + Another side length + x + 4(Another side length) - 4 + x = 59

Now, let's simplify the equation:
3x + 5(Another side length) - 4 = 59

We have two variables (x and Another side length) and two equations. We can solve this system of equations using substitution or elimination method. However, let's choose to solve for x by isolating it in the first equation.

x = 4(Another side length) - 4
x = 4Another side length - 4

Now substitute this value of x in the second equation:
3(4Another side length - 4) + 5Another side length - 4 = 59

Simplify the equation:
12Another side length - 12 + 5Another side length - 4 = 59
17Another side length - 16 = 59

Now, isolate Another side length:
17Another side length = 59 + 16
17Another side length = 75
Another side length = 75/17

Substitute this value of Another side length in the first equation to find x:
x = 4(Another side length) - 4
x = 4(75/17) - 4
x = 300/17 - 68/17
x = 232/17

So the lengths of the sides of the kite are:
One side length = x = 232/17 cm
Another side length = 75/17 cm