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Lakeside Street and Kingwood Avenue intersect. If Lakeside Street is $15\,\text{meters}$ wide and Kingwood Avenue is $8\,\text{meters}$ wide, what is the distance between two opposite corners of the intersection? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem: word problems

Full solution

Q. Lakeside Street and Kingwood Avenue intersect. If Lakeside Street is

15\,\text{meters}

wide and Kingwood Avenue is

8\,\text{meters}

wide, what is the distance between two opposite corners of the intersection?

\newline

\_\_\_\_\_

meters

Recognize Rectangle Intersection: Recognize the intersection as the corner of a rectangle with Lakeside Street and Kingwood Avenue as the lengths of the sides.
Use Pythagorean Theorem: Use the Pythagorean Theorem to find the diagonal (distance between opposite corners). The formula is $a^2 + b^2 = c^2$ , where $c$ is the diagonal.
Calculate Diagonal: Plug in the values for Lakeside Street ( $15$ meters) and Kingwood Avenue ( $8$ meters) into the formula: $15^2 + 8^2 = c^2$ .
Plug in Values: Calculate the squares: $15^2 = 225$ and $8^2 = 64$ .
Calculate Squares: Add the squares together: $225 + 64 = 289$ .
Find Square Root: Find the square root of $289$ to solve for $c$ : $\sqrt{289} = 17$ .

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