Finding Right Triangles
Question 4: Do the side lengths 3, 4, and 5 create a right triangle?
No!
Solve for the hypotenuse when the leg lengths are 3 and 4
5
2/4 as a decimal
0.5
3
π (pi)
Irrational
Do the side lengths 4, 5, and 6 make a right triangle?
Yes!
42+32=52
Solve for the hypotenuse when the leg lengths are 5 and 12
13
1/3 as a decimal
0.333333333...
Square root of 36
6
Rational
Do the side lengths 6, 8, and 10 work for a right triangle?
Yes!
36+64=100
Solve for a leg when the hypotenuse is 15 and one of the legs is 12
9
2/11 as a decimal
0.1818181818
Cube root of 8
2
The square root of 2
Irrational
Do the side lengths square root of 3, square root of 4, and square root of 5 work for a right triangle?
No!
3+4=7, not 5
Solve for a leg when the hypotenuse is 25 and a leg is 6
24.2693...
23/4 as a decimal
5.75
3.872983...
The square root of 225
Rational (=15)
Do the side lengths square root of 2, square root of 3, and square root of 5 work for a right triangle?
Yes!
2+3=5
Solve for the hypotenuse when the legs are 15 and 8
17
16/9 as a decimal
1.77777...
Cube root of 25
2.9240177...
10/7
Rational!
Every fraction is rational