Question

elias and jerry have two options to walk from their school to a corner store. • option 1: walk 660 feet due north and then turn and walk due west • option 2: walk 1,190 feet on a straight path directly to the store through a park how many feet due west will elias and jerry walk if they choose option 1? round your answer to the nearest whole number.

Explanation:

Step1: Identify the problem as a right - triangle problem

The two - part walk in option 1 forms the two legs of a right - triangle, and the straight - path in option 2 is the hypotenuse. Let the north - ward distance be $a = 660$ feet, the west - ward distance be $b$, and the hypotenuse $c=1190$ feet. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$.

Step2: Rearrange the Pythagorean theorem to solve for $b$

We can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute the values of $a$ and $c$

Substitute $a = 660$ and $c = 1190$ into the formula: $b=\sqrt{1190^{2}-660^{2}}=\sqrt{(1190 + 660)(1190 - 660)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $(1190 + 660)=1850$ and $(1190 - 660)=530$. Then $b=\sqrt{1850\times530}=\sqrt{980500}$.

Step4: Calculate the value of $b$

$b=\sqrt{980500}\approx990.2$.

Step5: Round to the nearest whole number

Rounding $990.2$ to the nearest whole number gives $990$.

Answer:

$990$