Question

Select the three lengths that could be the sidesof a right triangle.7 feet15 feet24 feet25 feet

Answer 1

The sides of a right triangle follow two rules that we need to fit to solve this question.

Let's call the hypotenuse 'h', and the legs 'a' and 'b'. We need to have the following relations:

`\begin{gathered} a+b>h \\ a^2+b^2=h^2 \\ h>a,h>b \end{gathered}`

To solve this we need to test the permutations of the values we have. For example, let's say we have a = 7 and b = 15.

`7+15=22`

From this, we can't fit 24 or 25 in the first rule, then 7 and 15 can't be the legs of a right triangle with those values.

Now, let's test for a = 7 and b = 24.

`\begin{gathered} 7+24=31 \\ 25<31 \end{gathered}`

Let's check if it fits the second rule.

`\begin{gathered} 7^2+24^2=49+576=625 \\ \sqrt[]{625}=25 \end{gathered}`

It fits! Then, our right triangle(with this set of values) have legs 7 and 24, and hypotenuse equals to 25.