Serena is creating a stained glass windowpane that will be 7.8 inches by 5.5 inche

Question

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?

Answer 1

Hi, Jenny.

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.

 

Answer 2

We are given that the dimensions of the rectangle are 7.8 in by 5.5 in. If we draw a diagonal line from one corner of the rectangle to its adjacent corner, we have the 2 triangles fused to make this rectangle with this diagonal line being the hypotenuse (label the hypotenuse 'c'). We know that the length of one leg of these triangles is 7.8 inches (label this leg 'a') and the length of the other leg of the triangle is 5.5 inches (label this leg 'b'). 

With this, we have the following:

     a = 7.8 ,     b = 5.5 ,     c = ?

Since the triangles are fused to make a rectangle, we can conclude that the angle between a and b is a right angle. From this, we can use the pythagorean theorem to find the length of the hypotenuse (c) using the following formula:

     a² + b² = c²

     (7.8)² + (5.5)² = c²

     60.84 + 30.25 = c²

     91.09 = c²

     √(91.09) = √(c²)

     9.5 = c

The perimeter of the triangle is equal to the sum of all its sides:

     p = a + b + c 

     p = 7.8 + 5.5 + 9.5

     p = 22.8

Thus, the perimeter of the triangle is 22.8 inches.