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Lacey is decorating a ballroom ceiling with garland. The width of the rectangular ceiling is $5$ meters and the diagonal distance from one corner to the opposite corner is $13$ meters. How much garland will Lacey need for the length of the ceiling? $\newline$ _____ meters

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Pythagorean theorem: word problems

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Q. Lacey is decorating a ballroom ceiling with garland. The width of the rectangular ceiling is

5

meters and the diagonal distance from one corner to the opposite corner is

13

meters. How much garland will Lacey need for the length of the ceiling?

\newline

_____ meters

Identify values: Step $1$ : Identify the known values and the unknown value. $\newline$ We know the width of the ceiling is $5$ meters and the diagonal is $13$ meters. We need to find the length of the ceiling, let's call it $L$ .
Apply Pythagorean Theorem: Step $2$ : Apply the Pythagorean Theorem. $\newline$ Since the ceiling forms a right triangle with the width and the diagonal, we use the formula: $\newline$ $Width^2 + Length^2 = Diagonal^2$ $\newline$ $5^2 + L^2 = 13^2$
Simplify and solve: Step $3$ : Simplify and solve for $L^2$ . $\newline$ $25 + L^2 = 169$ $\newline$ Subtract $25$ from both sides: $\newline$ $L^2 = 169 - 25$ $\newline$ $L^2 = 144$
Find length: Step $4$ : Solve for $L$ by taking the square root of $L^2$ . $L = \sqrt{144}$ $L = 12$

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