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Question
Rita draws the following shape and asks her sister to find the number of triangles in it. What is the correct number of triangles in the shape?
Rita draws the following shape and asks her sister to find the number of triangles in it. What is the correct number of triangles in the shape?
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Solution
The correct option is A 25
Let's label the figure:
The simple triangles are AIE, AIF, EIH, FIH, HJE, BJE, BJG, HJG, GHC, CHD, and FHD. There are such 11 triangles.
The triangles composed of two components each are AEF, EFH, AHE, AHF, BHE, BHG, BEG, and EGH. There are 8 such triangles.
The triangles composed of three components each are AHD, and BHC. There are 2 such triangles.
The triangles composed of four components each are AHB and EFG. There are 2 such triangles.
The triangles composed of seven components each are ACB and BDA. There are 2 such triangles.
So, total number of triangles in the given figure = 11 + 8 + 2 + 2 + 2 = 25
Let's label the figure:
The simple triangles are AIE, AIF, EIH, FIH, HJE, BJE, BJG, HJG, GHC, CHD, and FHD. There are such 11 triangles.
The triangles composed of two components each are AEF, EFH, AHE, AHF, BHE, BHG, BEG, and EGH. There are 8 such triangles.
The triangles composed of three components each are AHD, and BHC. There are 2 such triangles.
The triangles composed of four components each are AHB and EFG. There are 2 such triangles.
The triangles composed of seven components each are ACB and BDA. There are 2 such triangles.
So, total number of triangles in the given figure = 11 + 8 + 2 + 2 + 2 = 25
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