The polygons are similar but not necessarily drawn to scale, find the value of x
bigger polygon has 18, 18, and 15
smaller has 6, 6, and 2x-11
ASISTANCE REQUIERD ASAP
6/18 = (2x-11)/15
x=8
To find the value of x, we can set up a proportion between the corresponding sides of the similar polygons.
We know that the corresponding sides of similar polygons are in proportion, meaning that their ratios are equal. In this case, we can set up the ratio between the corresponding sides as:
(Length of corresponding side in the bigger polygon) / (Length of corresponding side in the smaller polygon) = (Ratio of the larger polygon) / (Ratio of the smaller polygon)
Let's denote the length of the corresponding side in the bigger polygon as 'a', and the length of the corresponding side in the smaller polygon as 'b'. The ratios of the larger polygon and the smaller polygon can be expressed as:
Ratio of the larger polygon = (18 + 18 + 15) / 3 = 51 / 3 = 17
Ratio of the smaller polygon = (6 + 6 + (2x - 11)) / 3
Now, we can set up the proportion:
a / b = 17 / [(6 + 6 + (2x - 11)) / 3]
To solve for x, we can cross-multiply and solve the resulting equation for x:
a * [(6 + 6 + (2x - 11)) / 3] = 17 * b
Simplifying further:
a * (2x + 1) = 51 * b
Now, substitute the given values:
18 * (2x + 1) = 51 * (2x - 11)
Solve this equation to find the value of x.
In order to find the value of x, we can equate the ratios of corresponding sides of the two similar polygons.
Let's start by comparing the corresponding sides of the polygons. In the larger polygon, the side lengths are 18, 18, and 15. In the smaller polygon, the side lengths are 6, 6, and 2x - 11.
We can set up the following ratios:
18 / 6 = 18 / 6 = 15 / (2x - 11)
To solve for x, we can cross-multiply and solve the resulting equation:
18(2x - 11) = 15 * 6
36x - 198 = 90
Adding 198 to both sides of the equation:
36x = 90 + 198
36x = 288
Dividing both sides by 36:
x = 288 / 36
Simplifying, we find:
x = 8
Therefore, the value of x is 8.