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Math- Make a Crazy Quilt?
Vanessa and Sarah are making a quilt with 12 qual sections. Each section is shaped like a rectangle and all 12 sections have the same dimensions. The length of each section is twice its width.
The width of the entire quilt will be 4 sections wide and the length of the entire quilt will be 3 sections long
Each section of the quilt has
2 right triangles each of which has a hypotenuse of 10 inches and another side of 8 inches
an isosceles triangle with an area of 48 square inches and a base of 16 inches
a rectangle with an area of 24 square inches and one side of 6 inches
2 squares with an area of 36 square inches each
a rectangle with an area of 96 square inches and one side of 8 inches
What will be the final dimensions ( length and width) of the quilt?
Fun problem!
Start by finding the area of each section.
2 right triangles: These are 3:4:5 triangles, expanded by a factor of 2. Area: (1/2)(6)(8) = 24 each. Two of them = 48 in².
All the rest of the parts have their areas given. The actual dimensions aren't needed.
Total area of each section = 2(24) + 48 + 24 + 2(36) + 96 = 288 in².
The only way for a section of 288 in² to be twice as long as it is wide is for its dimensions to be 24 in long by 12 in wide.
The entire quilt is 4 sections wide: 4x12 = 48 in.
The entire quilt is 3 sections long: 3x24 = 72 in.
...which could also be expressed as 4 ft x 6 ft.
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