Kyle wants to form rectangles using straws.he has two straws of 6 inches long, two straws 4 inches long, and two straws 2 inches long.using four straws attached at the ends, how many different rectangles can Kyle form¿ what are the perimeters of the rectangles¿
1. 6x4 in., P = 2*6 + 2*4 = 20 in.
2. 6*2 in., P = 2*6 + 2*2 = 16 in.
3. 4x2 in., P = 2*4 + 2*2 = 12 in.
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6-4 20in 6-2 16in 4-2 12in
WhAt is the answer
Well, Kyle certainly has a lot of options! Let's see how many different rectangles he can make.
First, let's look at the two 6-inch straws. He can use them as the length or the width of the rectangle. So that's two options.
Now, he has to choose two straws for the other side of the rectangle. He can choose from the remaining four straws: two 4-inch ones, and two 2-inch ones.
If he chooses two 4-inch straws, he can attach them to the ends of the 6-inch straws to create a rectangle.
If he chooses two 2-inch straws, he can attach them to the ends of the 6-inch straws to create a smaller rectangle.
Since the length and width of the rectangle can be interchanged, we can count these combinations twice (once with length as 6 inches and width as 4 inches, and once with length as 4 inches and width as 6 inches).
So, in total, Kyle can make 2 rectangles: one with 6-inch length and 4-inch width, and one with 4-inch length and 6-inch width.
Now, let's calculate their perimeters:
For the first rectangle, with length 6 inches and width 4 inches: Perimeter = 2 * (Length + Width) = 2 * (6 + 4) = 2 * 10 = 20 inches.
For the second rectangle, with length 4 inches and width 6 inches: Perimeter = 2 * (Length + Width) = 2 * (4 + 6) = 2 * 10 = 20 inches.
So, both rectangles have a perimeter of 20 inches. Happy rectangle making, Kyle!
To find out how many different rectangles Kyle can form and their perimeters, we need to consider the lengths of the available straws.
The formula for the perimeter of a rectangle is: P = 2(length + width).
Since Kyle can only use four straws at a time, he needs to choose two as the length and two as the width. Let's break down the possibilities:
1. Using the 6-inch straws:
a) Using two 6-inch straws as the length and two 6-inch straws as the width: P = 2(6 + 6) = 24 inches.
b) Using two 6-inch straws as the length and two 4-inch straws as the width: P = 2(6 + 4) = 20 inches.
c) Using two 6-inch straws as the length and two 2-inch straws as the width: P = 2(6 + 2) = 16 inches.
2. Using the 4-inch straws:
a) Using two 4-inch straws as the length and two 4-inch straws as the width: P = 2(4 + 4) = 16 inches.
b) Using two 4-inch straws as the length and two 2-inch straws as the width: P = 2(4 + 2) = 12 inches.
3. Using the 2-inch straws:
a) Using two 2-inch straws as the length and two 2-inch straws as the width: P = 2(2 + 2) = 8 inches.
So, Kyle can form a total of 5 different rectangles, and their respective perimeters are as follows:
1. Rectangle 1: P = 24 inches.
2. Rectangle 2: P = 20 inches.
3. Rectangle 3: P = 16 inches.
4. Rectangle 4: P = 12 inches.
5. Rectangle 5: P = 8 inches.