To solve the exercise, it is useful to first draw the situation posed by the statement:
As you can see in the situation, a right triangle is formed. So, you can use the Pythagorean Theorem to find the distance between home and market:
So, you have
![\begin{gathered} a=32\operatorname{km} \\ b=24\operatorname{km} \\ c=? \end{gathered}]()
![\begin{gathered} a^2+b^2=c^2 \\ (32km)^2+(24km)^2=c^2 \\ 1024\operatorname{km}+576km^2=c^2 \\ 1600\operatorname{km}=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{1600\operatorname{km}^2}=\sqrt[]{c^2} \\ 40\operatorname{km}=c \end{gathered}]()
Therefore, if she takes a boat across the lake directly toward the market, her home is 40 kilometers from the market.