Question

Which set of side lengths can be used to form a right triangle

A.4,5,6
B.2,3,4
C.10,20,30
D.30,40,50

Answer 1

d

Explanation:

Answer 2

D. 30, 40, 50

Explanation:

For a right triangle the the values for the three sides we pick must satisfy the Pythagorean theorem:

`a^2+b^2=c^2`

where a and b are the two sides, c is the hypotenuse of the right triangle.

Notice that c is always going to be greater than a or b; this means that the largest number in our choices is the hypotenuse.

Let us check each of the choice to see if they satisfy the Pythagorean theorem:

Choice A. 4,5,6

`4^2+5^2\\eq 6^2`

this doesn't work.

Choice B. 2,3,4

`2^2+3^2\\eq 4^2`

this doesn't work either.

Choice C. 10, 20, 30

`10^2+20^2\\eq 30^2`

nope

Choice D. 30, 40, 50.

`30^2+40^2=50^2`

it works!

So our answer is Choice D. 30, 40, 50.