Which set of measurements could be sidelights of a right triangle

Question

A. 0.5cm,0.8cm,0.4cm

B. 0.3cm,0.5cm,0.4cm

C. 0.6cm,0.5cm,0.3cm

D. 0.3cm,0.6cm,0.7cm

Answer 1

By definition, a right triangle has one 90 degree angle and the pythagorean formula applies: a² + b² = c².  That means that the square root of the sum of squares of the 2 shorter sides equals the longer side (hypoteneuse).  So try plugging the numbers from each of the groups above into the pythagorean equation:

A. (0.5² + 0.4²)^.5 = 0.64, which is not equal to 0.8 so A. is not the answer

B. (0.3² + 0.4²)^.5 = 0.5, so B is the answer.  Also, a common type of right triangle is a 3, 4, 5 triangle which this one is (0.3, 0.4, 0.5).

C. (0.3² + 0.5²)^.5 = 0.58 which is not equal to 0.6 so C. is not the answer

D. (0.3² + 0.6²)^.5 = 0.67 which is not equal to 0.7 so D. is not the answer

Answer 2

The trick here is to use the Pythagorean Theorem: A² + B² = C²

This concept is designed specifically for right triangles, so you can use it to easily guess-and-check which answer works.

 

As we know, the hypotenuse of a right triangle is always the longest side. So, which choice correctly fulfills A² + B² = C²?

 

A: False

(0.5)² + (0.4)² = (0.8)²

0.25 + 0.16 = 0.64

0.41 = 0.64

 

B: TRUE!

(0.3)² + (0.4)² = (0.5)²

0.09 + 0.16 = 0.25

0.25 = 0.25

 

C: False

(0.3)² + (0.5)² = (0.6)²

0.09 + 0.25 = 0.36

0.34 = 0.36

 

D: False

(0.3)² + (0.6)² = (0.7)²

0.09 + 0.36 = 0.49

0.45 = 0.49

 

Another trick to find the answer to this problem is to remember that a 3-4-5 triangle (as in a triangle with sides that follow the ratio 3-4-5) will always be a right triangle. For example, if you had a triangle with sides of 6 inches, 8 inches, and 10 inches (the 10-inch side being the hypotenuse), you would know automatically that this must be a right triangle because it follows the 3-4-5 convention.