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Lila takes a $52$ -centimeter by $39$ -centimeter rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to the diagonally opposite corner. Now Lila has two equally sized triangles of plywood. What is the perimeter of each triangle? $\newline$ _____ centimeters

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Pythagorean Theorem and its converse

Full solution

Q. Lila takes a

52

-centimeter by

39

-centimeter rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to the diagonally opposite corner. Now Lila has two equally sized triangles of plywood. What is the perimeter of each triangle?

\newline

_____ centimeters

Calculate Diagonal Length: Calculate the length of the diagonal using the Pythagorean Theorem. $\newline$ $52^2 + 39^2 = \text{diagonal}^2$ $\newline$ $2704 + 1521 = \text{diagonal}^2$ $\newline$ $4225 = \text{diagonal}^2$ $\newline$ $\text{diagonal} = \sqrt{4225}$ $\newline$ $\text{diagonal} = 65 \, \text{cm}$
Find Triangle Perimeter: Determine the perimeter of one triangle. $\newline$ Perimeter = $52\,\text{cm} + 39\,\text{cm} + 65\,\text{cm}$ $\newline$ Perimeter = $156\,\text{cm}$

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