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A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is $10\,\text{meters}$ and the distance between the gopher's holes is $26\,\text{meters}$ . How wide is the yard? $\newline$ $\_\_\_\_\_$ meters

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Pythagorean theorem

Full solution

Q. A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is

10\,\text{meters}

and the distance between the gopher's holes is

26\,\text{meters}

. How wide is the yard?

\newline

\_\_\_\_\_

meters

Given Triangle Information: We have a right triangle with one leg being the length of the yard ( $10$ meters) and the hypotenuse being the distance between the gopher's holes ( $26$ meters). We need to find the other leg, which is the width of the yard.
Pythagorean Theorem: Using the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ is the length, $b$ is the width, and $c$ is the diagonal.
Substitute Values: Plug in the known values: $10^2 + b^2 = 26^2$ .
Calculate Squares: Calculate the squares: $100 + b^2 = 676$ .
Solve for $b^2$ : Subtract $100$ from both sides to solve for $b^2$ : $b^2 = 676 - 100$ .
Calculate Difference: Calculate the difference: $b^2 = 576$ .
Solve for $b$ : Take the square root of both sides to solve for $b$ : $b = \sqrt{576}$ .
Final Calculation: Calculate the square root: $b = \sqrt{24}$ .

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