Can you please help me answer these and explain? Please?
Determine whether the given lengths can be side lengths of a right triangle.
1) 6ft, 10ft, 12ft
2) 10in, 24in, 26in
3) 20m, 21m, 29m
4) 15cm, 17cm, 21cm
5) 14ft, 22.5ft, 26.5ft
6) 12yd, 35yd, 38yd
a^2+b^2=c^2
the largest side/hypothenuse is c
a and b are the other two sides
1) 6^2+10^2 = c^2
check to see if that's true or not
Does 5ft, 12ft, and 15ft make a right triangle ?
Of course! I'd be happy to help you with these questions and explain how to determine whether the given lengths can be side lengths of a right triangle.
To determine whether the given lengths can be side lengths of a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Let's go through each set of lengths one by one:
1) 6ft, 10ft, 12ft
We can check if these lengths satisfy the Pythagorean theorem:
12^2 = 6^2 + 10^2
144 = 36 + 100
144 = 136
Since the equation is not true, these lengths cannot be the side lengths of a right triangle.
2) 10in, 24in, 26in
Let's check if these lengths satisfy the Pythagorean theorem:
26^2 = 10^2 + 24^2
676 = 100 + 576
676 = 676
Since the equation is true, these lengths can indeed be the side lengths of a right triangle.
3) 20m, 21m, 29m
Now, let's check if these lengths satisfy the Pythagorean theorem:
29^2 = 20^2 + 21^2
841 = 400 + 441
841 = 841
Since the equation is true, these lengths can indeed be the side lengths of a right triangle.
4) 15cm, 17cm, 21cm
Let's check if these lengths satisfy the Pythagorean theorem:
21^2 = 15^2 + 17^2
441 = 225 + 289
441 = 514
Since the equation is not true, these lengths cannot be the side lengths of a right triangle.
5) 14ft, 22.5ft, 26.5ft
Now, let's check if these lengths satisfy the Pythagorean theorem:
26.5^2 = 14^2 + 22.5^2
702.25 = 196 + 506.25
702.25 = 702.25
Since the equation is true, these lengths can indeed be the side lengths of a right triangle.
6) 12yd, 35yd, 38yd
Let's check if these lengths satisfy the Pythagorean theorem:
38^2 = 12^2 + 35^2
1444 = 144 + 1225
1444 = 1369
Since the equation is not true, these lengths cannot be the side lengths of a right triangle.
So, out of the given sets of lengths:
- 10in, 24in, 26in
- 20m, 21m, 29m
- 14ft, 22.5ft, 26.5ft
These sets of lengths can be the side lengths of a right triangle.