Answer with explanation:
According to Pythagorean Theorem if in a right triangle the two legs of a right triangle are a and b and the hypotenuse is denoted by c then we have:
[tex]c^2=a^2+b^2[/tex]
Ques 1)
By Pythagorean Theorem we have:
[tex](440)^2=(305)^2+a^2\\\\i.e.\\\\193600=93025+a^2\\\\\\a^2=193600-93025\\\\\\a^2=100575\\\\\\a=317.1356\ units[/tex]
To the nearest tenth we have: a=317.1
Ques 2)
By Pythagorean Theorem we have:
[tex](415)^2=(390)^2+b^2\\\\i.e.\\\\172225=152100+b^2\\\\\\b^2=172225-152100\\\\\\b^2=20125\\\\\\b=141.8626\ units[/tex]
To the nearest tenth we have: b=141.9
Ques 3)
By Pythagorean Theorem we have:
[tex]c^2=(625)^2+(450)^2\\\\\\c^2=593125\\\\\\c=770.1460[/tex]
To the nearest tenth we have: c=770.1
Ques 4)
By Pythagorean Theorem we have:
[tex](515)^2=(380)^2+d^2\\\\\\d^2=120825\\\\\\d=347.5989[/tex]
To the nearest tenth we have: d=347.6
Ques 5)
By Pythagorean Theorem we have:
[tex](700)^2=(400)^2+e^2\\\\\\e^2=330000\\\\\\e=574.4562[/tex]
To the nearest tenth we have: e=574.4
Ques 6)
By Pythagorean Theorem we have:
[tex](750)^2=(500)^2+f^2\\\\\\f^2=312500\\\\\\f=559.0169[/tex]
To the nearest tenth we have: f=559
Ques 7)
By Pythagorean Theorem we have:
[tex](g)^2=(250)^2+(250)^2\\\\\\g^2=125000\\\\\\g=353.5533[/tex]
To the nearest tenth we have: g=353.6
Ques 8)
By Pythagorean Theorem we have:
[tex](400)^2=(325)^2+h^2\\\\\\h^2=54375\\\\\\h=233.1844[/tex]
To the nearest tenth we have: h=233.2
Ques 9)
By Pythagorean Theorem we have:
[tex](i)^2=(300)^2+(400)^2\\\\\\i^2=250000\\\\\\i=500[/tex]
To the nearest tenth we have: i=500
Ques 10)
A Pythagorean triple is the set of three positive integers a,b and c such that it satisfy:
[tex]c^2=a^2+b^2[/tex]
Hence, we among the given above options the Pythagorean triple are:
The last option form i.e. the triangle whose side is 300, 400 and i.
Also, the figure is attached to the answer.
