The mid points of a triangle are joined. Forming a second triangle, a third triangle is formed joining the midpoints of the second and the process continued infinitely. If the area of the first triangle is 24 units, then find the sum of areas of all triangles.

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Solution

The correct option is C 32
By graphical division, we see that the triangle can be broken into 4 smaller similar triangles, out of which, the one formed by joining the mid-points is one.

therefore, the common ratio of division = ¼ (Area is 1/4^th that of 1^st triangle)

S_∞ = = 32 units

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The mid points of a triangle are joined. Forming a second triangle, a third triangle is formed joining the midpoints of the second and the process continued infinitely. If the area of the first triangle is 24 units, then find the sum of areas of all triangles.

The correct option is C 32By graphical division, we see that the triangle can be broken into 4 smaller similar triangles, out of which, the one formed by joining the mid-points is one. therefore, the common ratio of division = ¼ (Area is 1/4th that of 1st triangle) S∞ = = 32 units

The correct option is C 32
By graphical division, we see that the triangle can be broken into 4 smaller similar triangles, out of which, the one formed by joining the mid-points is one.

therefore, the common ratio of division = ¼ (Area is 1/4^th that of 1^st triangle)

S_∞ = = 32 units