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Julian is creating a stained glass windowpane that will be $72$ centimeters by $21$ centimeters. To make the rectangular windowpane, Julian fuses together two triangles of colored glass. What is the perimeter of one triangle? $\newline$ _____ centimeters

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Pythagorean theorem

Full solution

Q. Julian is creating a stained glass windowpane that will be

72

centimeters by

21

centimeters. To make the rectangular windowpane, Julian fuses together two triangles of colored glass. What is the perimeter of one triangle?

\newline

_____ centimeters

Identify Dimensions: Identify the dimensions of the rectangle formed by the two triangles. The rectangle is $72\,\text{cm}$ by $21\,\text{cm}$ .
Calculate Triangle Diagonal: Calculate the length of the diagonal of one triangle, which will be the same as the rectangle's length since the diagonal divides the rectangle into two equal triangles. The diagonal is $72\,\text{cm}$ .
Calculate Triangle Perimeter: Calculate the perimeter of one triangle. The perimeter $P$ is the sum of all three sides of the triangle. $P = \text{side1} + \text{side2} + \text{diagonal}$ . Here, $\text{side1}$ is $21$ cm, $\text{side2}$ is $21$ cm, and the diagonal is $72$ cm.
Add Lengths for Perimeter: Add the lengths of the sides and the diagonal to find the perimeter. $P = 21\,\text{cm} + 21\,\text{cm} + 72\,\text{cm}$ .
Perform Addition: Perform the addition to find the perimeter. $P = 21 + 21 + 72 = 114$ cm.

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