Given that pentagon JKL MN is similar to pentagon STUVW, we can use the properties of similar figures to find the length of ST.
The relationship of corresponding sides in similar polygons means the ratios of their corresponding sides are equal. If we know the lengths of sides NJ, WS, and JK, we can set up a proportion to solve for ST.
From the information given:
- NJ = 4
- WS = 3
- JK = 5
Let’s denote the side ST that we want to find as X. Because the pentagons are similar, we can express the proportionality as:
Ratio = (JK / ST) = (NJ / WS)
Plug in the known values:
(5 / X) = (4 / 3)
Now, we can cross-multiply to solve for X:
5 * 3 = 4 * X
15 = 4X
Now, divide both sides by 4:
X = 15 / 4
X = 3.75
Thus, the length of ST is 3.75.