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what is the ratio of the area of the smaller triangle in relation to the area of the larger triangle?
5 answers
Unfortunately, as an AI text-based model, I cannot directly see or interpret images. To answer your question accurately, please provide a verbal description or detail of the image and its contents, or provide further context or specific measurements related to the triangles in question.
here are the areas of the small triangles.
1st (5,9),(2,3),(5,3)
2nd (12,6),(12,2),10,2)
1st (5,9),(2,3),(5,3)
2nd (12,6),(12,2),10,2)
To find the ratio of the area of the smaller triangle to the larger triangle, we need to calculate the areas of both triangles.
1st Triangle:
Given the coordinates (5, 9), (2, 3), and (5, 3), we can calculate the base and height of the triangle.
Base = distance between (5, 9) and (2, 3) = sqrt((2 - 5)^2 + (3 - 9)^2) = sqrt(9 + 36) = sqrt(45)
Height = distance between (2, 3) and (5, 3) = sqrt((5 - 2)^2 + (3 - 3)^2) = sqrt(9) = 3
Area of 1st Triangle = (1/2) * base * height = (1/2) * sqrt(45) * 3 = (3/2) * sqrt(45)
2nd Triangle:
Given the coordinates (12, 6), (12, 2), and (10, 2), we can calculate the base and height of the triangle.
Base = distance between (12, 6) and (12, 2) = 6 - 2 = 4
Height = distance between (12, 2) and (10, 2) = 10 - 12 = -2 (we take the absolute value)
Area of 2nd Triangle = (1/2) * base * height = (1/2) * 4 * 2 = 4
Therefore, the ratio of the area of the smaller triangle (1st Triangle) to the area of the larger triangle (2nd Triangle) is:
(3/2) * sqrt(45) / 4 ≈ 0.6614
1st Triangle:
Given the coordinates (5, 9), (2, 3), and (5, 3), we can calculate the base and height of the triangle.
Base = distance between (5, 9) and (2, 3) = sqrt((2 - 5)^2 + (3 - 9)^2) = sqrt(9 + 36) = sqrt(45)
Height = distance between (2, 3) and (5, 3) = sqrt((5 - 2)^2 + (3 - 3)^2) = sqrt(9) = 3
Area of 1st Triangle = (1/2) * base * height = (1/2) * sqrt(45) * 3 = (3/2) * sqrt(45)
2nd Triangle:
Given the coordinates (12, 6), (12, 2), and (10, 2), we can calculate the base and height of the triangle.
Base = distance between (12, 6) and (12, 2) = 6 - 2 = 4
Height = distance between (12, 2) and (10, 2) = 10 - 12 = -2 (we take the absolute value)
Area of 2nd Triangle = (1/2) * base * height = (1/2) * 4 * 2 = 4
Therefore, the ratio of the area of the smaller triangle (1st Triangle) to the area of the larger triangle (2nd Triangle) is:
(3/2) * sqrt(45) / 4 ≈ 0.6614
No the question need you to anser with those is,
what is the ratio of the area of the smaller tringle in relation to the area of the larger triangle.
what is the ratio of the area of the smaller tringle in relation to the area of the larger triangle.
Apologies for misunderstanding the question earlier. To find the ratio of the area of the smaller triangle to the larger triangle, we need to calculate the areas of both triangles using the given coordinates.
1st Triangle:
Given coordinates: (5, 9), (2, 3), and (5, 3)
Using the Shoelace formula or the determinant method, we can calculate the area of the 1st triangle:
Area of 1st Triangle = |(5*3 + 2*3 + 5*9) - (9*2 + 3*5 + 3*5)| / 2 = |(15 + 6 + 45) - (18 + 15 + 15)| / 2 = |66 - 48| / 2 = 18 / 2 = 9
2nd Triangle:
Given coordinates: (12, 6), (12, 2), and (10, 2)
Using the same method, we can calculate the area of the 2nd triangle:
Area of 2nd Triangle = |(12*2 + 12*2 + 10*6) - (6*12 + 2*10 + 2*12)| / 2 = |(24 + 24 + 60) - (72 + 20 + 24)| / 2 = |108 - 116| / 2 = 8 / 2 = 4
Therefore, the ratio of the area of the smaller triangle (1st Triangle) to the area of the larger triangle (2nd Triangle) is:
9 : 4 or 9/4
In other words, the area of the smaller triangle is 9/4 times the area of the larger triangle.
1st Triangle:
Given coordinates: (5, 9), (2, 3), and (5, 3)
Using the Shoelace formula or the determinant method, we can calculate the area of the 1st triangle:
Area of 1st Triangle = |(5*3 + 2*3 + 5*9) - (9*2 + 3*5 + 3*5)| / 2 = |(15 + 6 + 45) - (18 + 15 + 15)| / 2 = |66 - 48| / 2 = 18 / 2 = 9
2nd Triangle:
Given coordinates: (12, 6), (12, 2), and (10, 2)
Using the same method, we can calculate the area of the 2nd triangle:
Area of 2nd Triangle = |(12*2 + 12*2 + 10*6) - (6*12 + 2*10 + 2*12)| / 2 = |(24 + 24 + 60) - (72 + 20 + 24)| / 2 = |108 - 116| / 2 = 8 / 2 = 4
Therefore, the ratio of the area of the smaller triangle (1st Triangle) to the area of the larger triangle (2nd Triangle) is:
9 : 4 or 9/4
In other words, the area of the smaller triangle is 9/4 times the area of the larger triangle.
4 answers