Pythagorean Theorem - david, Thursday, July 15, 2010 at 2:10pm

EFG 3,6,9
HIJ 60,156,144
KLM 56,102,105
NOP 36,48,64

The following are the lengths of the sides of four triangles. Which is a right triangle?

a.Triangle EFG
b.Triangle HIJ
c.Triangle KLM
d.Triangle NOP

NOP

NOP is not correct.

To determine which triangle is a right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's calculate the values to see if they satisfy the Pythagorean Theorem:

a. Triangle EFG:
Side EF = 3, Side FG = 6, Side GE = 9
According to the Pythagorean Theorem, EF^2 + FG^2 = GE^2
Substituting the values, we get 3^2 + 6^2 = 9^2
Simplifying, we get 9 + 36 = 81
This equation is not true, so Triangle EFG is not a right triangle.

b. Triangle HIJ:
Side HI = 60, Side IJ = 156, Side HJ = 144
According to the Pythagorean Theorem, HI^2 + IJ^2 = HJ^2
Substituting the values, we get 60^2 + 156^2 = 144^2
Simplifying, we get 3600 + 24336 = 20736
This equation is not true, so Triangle HIJ is not a right triangle.

c. Triangle KLM:
Side KL = 56, Side LM = 102, Side KM = 105
According to the Pythagorean Theorem, KL^2 + LM^2 = KM^2
Substituting the values, we get 56^2 + 102^2 = 105^2
Simplifying, we get 3136 + 10404 = 11025
This equation is true, so Triangle KLM satisfies the Pythagorean Theorem and is a right triangle.

d. Triangle NOP:
Side NO = 36, Side OP = 48, Side NP = 64
According to the Pythagorean Theorem, NO^2 + OP^2 = NP^2
Substituting the values, we get 36^2 + 48^2 = 64^2
Simplifying, we get 1296 + 2304 = 4096
This equation is not true, so Triangle NOP is not a right triangle.

Therefore, the answer is c. Triangle KLM.