The length of the hypotenuse (x) is an irrational number between 6 and 8. Both legs have measures that are whole numbers. Illustrate a model for at least one possible set of measures for the sides of the right triangle
Answers
Given : The length of the hypotenuse (x) is a irrational number between 6 and 8
Both legs have measures that are whole numbers
To Find : illustrate a model for at least one possible set of measures for the sides of a right triangle
Solution:
P , B are Legs P , B ∈ W
P , B < x
6 < x < 8
=> 36 < x² < 64 x² ≠ 49 as x is irrational number
P² + B² = x²
=> 36 < P² + B² < 64 P² + B² ≠ 49
Lets take P = 1
36 < 1 + B² < 64
=> 35 < B² < 63
=> 6 ≤ B ≤ 7
( 1 , 6) and ( 1, 7) are 2 possible solutions
Lets take P = 2
36 < 4 + B² < 64
=> 32 < B² < 60
=> 6 ≤ B ≤ 7
( 2 , 6) and ( 2, 7) are another 2 possible solutions
Lets take P = 3
36 < 9 + B² < 64
=> 27 < B² < 55
=> 6 ≤ B ≤ 7
( 3 , 6) and ( 3, 7) are another 2 possible solutions
Lets take P = 4
36 < 16 + B² < 64
=> 20 < B² < 48
=> 5 ≤ B ≤ 6
( 4 , 5) and ( 4, 6) are another 2 possible solutions
Lets take P = 5
36 < 25 + B² < 64
=> 11 < B² < 39
=> 4 ≤ B ≤ 6
( 5 , 6) is 1 more possible solutions
All possible solutions
(1 , 6 , √37)
( 1, 7 , √50)
(2 , 6 , √40)
(2 , 7 , √53)
(3 , 6 , √45)
(3 , 7 , √58)
(4 , 5 , √41)
(4 , 6 , √52)
(5 , 6 , √61)
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