Serena is creating a stained glass windowpane that will be 7.8 inches by 5.5 inches. To make the rectangular windowpane, Serena fuses together two triangles of colored glass. What is the perimeter of one triangle?
To find perimeter of a triangle, we must have all three sides. We can assume the two triangles are right triangles since they make up a rectangle (window pane). Anytime we're working with right triangles, we may use the Pythagorean Theorem to help us find a missing side.
a^2 + b^2 = c^2
The c in the Pythagorean Theorem is always the longest side of the right triangle (the longest side is called the hypotenuse).
In this story, Serena knows the lengths of the two sides, but not the hypotenuse.
So let a= 7.8 and b = 5.5, and let's go...
(7.8)^2 + (5.5)^2 = c^2
60.84 + 30.25 = c^2
91.09 = c^2
Now find the square root of 91.09
√91.09 = 9.544108 etc
Now, we have all three sides of the triangle: 7.8 in, 5.5 in, and 9.5 in
Add these three together to get the perimeter.
My answer is 22.8 inches.