A quadrilateral has a perimeter of 207 units and one side measures 36 units. The lengths of the other three sides are in the ratio of 5:6:8. Find the lengths of the three missing sides.

45, 54, 72

Explanation:

In this case, a quadrilateral is like a square, with 4 sides but it's sides are longer than a square.

The perimeter of any geometrical figure is the sum of all the side's lenght, so, if we have the perimeter and the value of one side, we can deduce the lenght of the other sides because we have a data of the ratio. Let's first see how much is left on the missing sides.

P = a + b + c + d

207 = 36 + b + c + d

171 = a + b + c

This means that the sum of the other 3 sides is 171. We know that the ratio of those sides is 5:6:8, so the sum of these sides can be written like this, in function of those ratios:

171 = 5x + 6x + 8x

171 = 19x

x = 9

With this number we can now calculate the sides of the quadrilateral:

a = 5x = 5 * 9 = 45

b = 6x = 6 * 9 = 54

c = 8x = 8 * 9 = 72

Therefore the missing sides's lenght are:

Hope this helps