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Gwen bicycles $4$ miles west to get from her house to school. After school, she bicycles $3$ miles north to her friend Mason's house. How far is Gwen's house from Mason's house, measured in a straight line? $\newline$ $\_\_\_\_$ miles

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Pythagorean theorem: word problems

Full solution

Q. Gwen bicycles

4

miles west to get from her house to school. After school, she bicycles

3

miles north to her friend Mason's house. How far is Gwen's house from Mason's house, measured in a straight line?

\newline

\_\_\_\_

miles

Identify Legs of Triangle: Identify the legs of the triangle formed by Gwen's travel. Gwen travels $4$ miles west and $3$ miles north. These distances are the legs of a right triangle.
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the distance between Gwen's house and Mason's house. Let d be the distance. Using the formula: $\newline$ $d^2 = 4^2 + 3^2$
Calculate Squares of Legs: Calculate the squares of the legs: $\newline$ $4^2 = 16$ $\newline$ $3^2 = 9$ $\newline$ $16 + 9 = 25$ $\newline$ $d^2 = 25$
Find Distance: Find the value of d by taking the square root of $25$ : $\newline$ $d = \sqrt{25}$ $\newline$ $d = 5$

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