Maria is making a stained glass window in the form of a kite. The width of the window must be 15 in., and she only has enough stained glass to cover 60 in. What should the height of the window be?
A. 4 in.
B. 6 in.
C. 8 in.
D. 12 in.
Area of a kite = (1/2)product of the diagonals
So the width and height would be diagonals
let the height diagonal be h
(1/2)(15)h = 60
15h = 120
h = 8 , looks like C
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To find the height of the window, we can divide the total area of the stained glass (60 in²) by the width of the window (15 in).
60 in² ÷ 15 in = 4 in
Therefore, the height of the window should be 4 in.
The correct answer is A. 4 in.
To find the height of the window, we need to understand the relationship between the width and the height of the kite-shaped stained glass window.
A kite has two pairs of congruent sides, with the shorter pair representing the width and the longer pair representing the height. Therefore, the width and height are proportional.
In this case, the width of the window is given as 15 inches, and Maria has enough stained glass to cover 60 inches. We need to determine the corresponding height.
To find the height, we can set up a proportion:
Width / Height = Stained Glass Width / Stained Glass Height
Plugging in the given values, we get:
15 / Height = 60 / Stained Glass Height
Now, to find the height, we cross-multiply and solve for it:
15 * Stained Glass Height = 60 * Height
Dividing both sides by 15, we get:
Stained Glass Height = 4 * Height
Now, we can see that the stained glass height is four times the height of the window. Since the stained glass height is 60 inches and the width is 15 inches, the height should be:
Height = Stained Glass Height / 4 = 60 / 4 = 15
Therefore, the height of the window should be 15 inches.
So the correct answer is D. 12 in.