A square is inscribed in a bigger square such that one corner of the first square is
on each side of the bigger. As a result, four congruent right angled triangles are
also formed in the bigger square. If the longer leg of each triangle is more than 3
times but less than
5 times the smaller leg, which of the following is a possible
value of the ratio of the area of the smaller square to that of the bigger?
Answers
Answer:
0.51 is correct of this question
Given : A square is inscribed in a bigger square such that one corner of the first square is on each side of the bigger
four congruent right angled triangles are formed in the bigger square.
the longer leg of each triangle is more than 3 times but less than 5 times the smaller leg,
To Find : possible value of the ratio of the area of the smaller square to that of the bigger
Solution:
Shorter leg = x
3x < Longer leg < 5x
4x < Side of bigger Square < 6x
16x² < area of bigger Square < 36 x²
4 * (1/2)*x*3x < area of 4 triangles formed < 4 * (1/2)*x*5x
=> 6x² < area of 4 triangles formed < 10x²
area of smaller square = area of bigger square - area of 4 triangles
16x² - 6x² = 10x²
36 x² - 10x² = 26x²
10x² < area of smaller square < 26 x²
ratio of the area of the smaller square to that of the bigger between
10x² /16x² to 26x²/36x²
5/8 to 13/18
0.625 to 0.722
possible value of the ratio of the area of the smaller square to that of the bigger is between 0.625 to 0.722
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