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This is homework. I need help finding the answer to this question :)-example-1

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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:


\begin{gathered} a^2+b^2=c^2\Rightarrow\text{ Pythagorean Theorem formula} \\ \text{ Where a and b are the legs and} \\ c\text{ is the hypotenuse of the right triangle} \end{gathered}

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.

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