The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is
Question:
The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is
The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is
Options
Answer: 90
Explanation:
Problem: In triangle ABC, midpoints of sides AB, BC, AC are M, N, P respectively. Medians from A, B, C intersect the line segments MP, MN, NP at X, Y, Z respectively. Area of triangle ABC = 1440 sq cm. Find area of triangle XYZ. Step 1: Use the property of medians and lines joining midpoints Lines joining midpoints divide the triangle into smaller triangles. The triangle formed by intersections of medians with the lines joining midpoints is similar to ABC. It is known that area ratio of △ XYZ to △ ABC = 1/16. Step 2: Compute area of △ XYZ Area of △ XYZ= (16/1) ×1440=90 sq cm
Explanation:
Problem: In triangle ABC, midpoints of sides AB, BC, AC are M, N, P respectively. Medians from A, B, C intersect the line segments MP, MN, NP at X, Y, Z respectively. Area of triangle ABC = 1440 sq cm. Find area of triangle XYZ. Step 1: Use the property of medians and lines joining midpoints Lines joining midpoints divide the triangle into smaller triangles. The triangle formed by intersections of medians with the lines joining midpoints is similar to ABC. It is known that area ratio of △ XYZ to △ ABC = 1/16. Step 2: Compute area of △ XYZ Area of △ XYZ= (16/1) ×1440=90 sq cm
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