Final answer:
To find the length of bar (PQ) in similar pentagons ABCDE and PQRST, we use the fact that they have proportional side lengths. The length of bar (PQ) is equal to the length of side BC in the pentagons.
Step-by-step explanation:
To find the length of bar (PQ) in pentagons ABCDE and PQRST, we need to use the fact that they are similar. Similar polygons have proportional side lengths. Let's say the length of bar (PQ) is represented as x.
Since the pentagons are similar, the ratio of corresponding side lengths is the same. In this case, the ratio of the lengths of sides PQ and AB is equal to the ratio of the lengths of the corresponding sides in the two pentagons.
Therefore, we can write the proportion:
PQ / AB = QR / BC
By substituting the given values, we get:
x / 3x = QR / BC
Simplifying the equation, we find:
x = QR / BC * 3x
To solve for x, we can cancel out the 3x on both sides:
1 = QR / BC
Now, we have QR = BC, so the length of bar (PQ) is equal to the length of side BC.