Question

Bhaskar went for hiking with scouts’ team and there the scouts were given a task to build tentswith the help of bamboos, ropes and canvas. The frame of the tent that Bhaskar prepared was of pyramid shape. To make it sturdier Bhaskar thought that he should fix a wooden stick on the triangular sides of the tent and fix the wooden stick at the mid points of the sides of two sides of the triangle. The distance between the end point of the bamboos on the sides was 3 m.Due to lack of even length bamboo sticks Bhaskar the triangles on the edges of tent were not congruent. Look into the figure of Bhaskar’s tent and answer the following questions. ( a ) To make tent sturdy Bhaskar used bamboo IJ in the back part of the tent. What length of bamboo shall he use so that it should be fixed exactly? ( b ) Using which property of triangles Bhaskar was able to find the length of GH and IJ. ( c ) Here BC: EF = 3: 9, then what will be the ratio of area of triangle ABC to area of triangle DEF. ( d ) What is the value of ratio AG : GB?​

Answer 1

Answer:

by mid point theoram half of EF=9 so IJ will be 4.5cm

Answer 2

A) Length of IJ = 4.5 m

B)Property by which property Bhaskar found the length of IJ and GH is by basic proportionality theorem

C) Ratio of triangle ABC to the area of triangle DEF is 9:81

D) ratio AG : GB = 1:9

Given:

Distance between the endpoint of the bamboos on the sides = 3 m

BC: EF = 3: 9

Find:

a) Length of IJ

b)Property by which property Bhaskar found the length of IJ and GH

c)The ratio of triangle ABC to the area of triangle DEF

d)ratio AG: GB

Solution:

a) IJ = 4.5 m according to the mid-point theorem.

In a triangle, the line joining the mid point of two sides of the triangle will be parallel to the third side and will be half the length of the third side.

As the third side EF = 9, IJ = 9/2 = 4.5 m

b) Basic proportionality theorem was used to find the length of GH and IJ

According to the proportionality theorem, the ratio of corresponding sides of any two equiangular triangles is the same.

Using this theory length of IJ and GH can be found.

The midpoint theorem can also be considered as the answer because it is a special case of the proportionality theorem.

c) 9: 81 is the ratio of the area of triangle ABC the  to the area of triangle DEF

d) 1: 9 using area proposition theorem

That is the area of triangles with the same base and same parallels are equal in area.

Length of IJ = 4.5 m

Property by which property Bhaskar found the length of IJ and GH is by basic proportionality theorem

The ratio of triangle ABC to the area of triangle DEF is 9:81

Ratio AG : GB = 1:9

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