Final answer:
To find the value of x, we set up a ratio equation based on the corresponding sides of the similar polygons.
Step-by-step explanation:
In the given question, it is stated that PQR is similar to UTV. Similar polygons have corresponding angles that are equal and corresponding sides that are proportional. This means that the ratio of the lengths of the corresponding sides is equal. In this case, we have:
PQ / UT = QR / TV = PR / UV. The given information tells us that PQ = 14, QR = 8, UT = x + 6, and TV = x - 3.
To find the value of x, we can set up an equation using the ratios:
14 / (x + 6) = 8 / (x - 3).
Cross-multiplying, we get:
8(x + 6) = 14(x - 3).
Simplifying and solving for x, we get:
8x + 48 = 14x - 42.
Subtracting 8x and adding 42 to both sides, we get:
48 + 42 = 14x - 8x.
Combining like terms, we have:
90 = 6x.
Dividing by 6, we get:
x = 15.