Question

In a regular triangle with the side of 10 cm a new triangle is inscribed by connecting the midpoints of the sides with straight lines. Then another triangle is inscribed in the obtained triangle using the same method, and so on without bound. Find the limit​

Answer 1

Answer:

Answer=

The mid-points of its sides are joined to from another triangle whose mid-points are joined to from another triangle. This process continues indefinitely.

Side of 2nd equilateral triangle =12cm ( line segment joining mid-point of two sides of a triangle is parallel to third side and half of it ).

Similarly, side of third equilateral triangle =6cm.... sides are 3,1,5,

4

3

.

Perimeter of 1st triangle =24=24+24=72cm

Perimeter of 2nd triangle =12+12+12=36cm

Perimeter of 3rd triangle =6+6+6=18cm.

Sum of perimeter of all triangles =72+36+18+9+

2

9

+

4

9

This is a GP series where,

common ratio =

72

36

=

2

1

Sum of an infinity GP =

1−r

a

=

1−

2

1

72

=72×2

=144.

Hence, the answer is 144.

Answer 2

There are two types of boxes containing mangoes. Each box of the larger type contains 2 more mangoes than the number of mangoes contained in 6 boxes of the smaller type. Each larger box contains 200 mangoes. Find the number of mangoes contained in the smaller box

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