Let's break down the situation:
Dahlia received $525 for her birthday.
She used one third of her birthday money to buy new boots. Calculating one third of $525: \[ \frac{525}{3} = 175 \]
So, Dahlia spent $175 on boots.
Now, we need to find out how much money she had left after buying the boots: \[ 525 - 175 = 350 \]
Dahlia then used the remaining money to purchase a new laptop. According to the information, the cost of the laptop was $175.
Since she has $350 left after buying the boots, and the laptop costs $175, it is indeed possible for her to buy the laptop.
Therefore, the statement that the cost of the laptop was $175 is true.