The pair of polygons is similar. Find the value of x.
Two polygons are shown. Each polygon has 5 sides.The top and bottom segments of each polygon are parallel. An obtuse angle is created by the left 2 sides on each polygon and a right segment connects the shorter top to the longer bottom.
On the larger polygon, the lower left segment is marked 30 inches and the right segment is marked 75 inches. On the smaller polygon the lower left segment is marked 12 inches and the right segment is marked x.
(1 point)
Responses
187.5 in.
187.5 in.
12 in.
12 in.
30 in.
30 in.
37.5 in.
37.5 in.
The two polygons are similar, so the ratio of corresponding sides is equal.
In this case, the ratio of the length of the lower left segment in the larger polygon to the smaller polygon is 30/12 = 2.5
Therefore, the length of the right segment in the smaller polygon (marked x) can be found by multiplying 2.5 by 75 (the length of the right segment in the larger polygon):
2.5 * 75 = 187.5
Therefore, the value of x is 187.5 inches.
So, the correct response is: 187.5 in.