Respuesta :
The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.
Step-by-step explanation:
The measurements are,
7cm, 11cm, 54cm, 60cm, 61cm, 65cm
Step:1
To check the right angle triangle, Pythagorean theorem can be used.
For a Pythagorean theorem,
[tex]Side^{2} + Side^{2} = Hypotenuse^{2}[/tex]..........................(1)
The side values are lower than the hypotenuse,
[tex]c=\sqrt{a^{2}+b^{2} }[/tex]...................................(2)
Where,
a,b - side values
c - Hypotenuse
For right angle triangle, c > a, b
Alternative : 1
Take, a = 7cm, b = 11cm
From eqn (2),
[tex]c = \sqrt{7^{2}+11^{2} }[/tex] = [tex]\sqrt{170}[/tex] = 13.04
The above value is not equal to the any one of the values of ( 54cm. 60cm, 61cm, 65cm ), So its not an sides of right triangle.
Alternative : 2
Take, a = 7cm, b = 54cm
From eqn (2),
[tex]c = \sqrt{7^{2}+54^{2} }[/tex] = [tex]\sqrt{2965}[/tex] = 54.45
The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.
Alternative : 3
Take, a = 7cm, b = 60cm
From eqn (2),
[tex]c = \sqrt{7^{2}+60^{2} }[/tex] = [tex]\sqrt{3649}[/tex] = 60.406
The above value is not equal to the any one of the values of (61cm, 65cm ), So its not an sides of right triangle.
Alternative : 4
Take, a = 7cm, b = 61cm
From eqn (2),
[tex]c = \sqrt{7^{2}+61^{2} }[/tex] = [tex]\sqrt{3770}[/tex] = 61.40
The above value is not equal to the values of (65cm ), So its not an sides of right triangle.
Alternative : 5
Take, a = 11cm, b = 54cm
From eqn (2),
[tex]c = \sqrt{11^{2}+54^{2} }[/tex] = [tex]\sqrt{3037}[/tex] = 55.1089
The above value is not equal to the any one of the values of (60cm, 61cm, 65cm ), So its not an sides of right triangle.
Alternative : 6
Take, a = 11cm, b = 60cm
From eqn (2),
[tex]c = \sqrt{11^{2}+60^{2} }[/tex] = [tex]\sqrt{3721}[/tex] = 61
The above value is equal to the values of (61cm ), So its an sides of right triangle. The three sides are 11, 60 and 61.
Step:2
Check for solution,
[tex]11^{2} + 60^{2} = 61^{2}[/tex]
[tex]3721=3721[/tex]
Result:
The side lengths of a right triangle is 11cm, 60cm and 61cm, that could be selected from the given measurements.
