Question

In a right triangle, one leg measures 4 inches and the other leg measures 6 inches. What is the length of the hypotenuse in inches? 

A. 52   B. 10   C. 2√ 13    D. √ 52

Answer 1

the length of the hypotenuse in inches is 2 square root 13

Answer 2

The answer is C.
`2√(13)`
`in^2`.

Explanation:

In order to determine the length of the hypotenuse, we have to know the pythagoras theorem.

The Pythagorean Theorem is a formula relating the lengths of the three sides of a right triangle.

If we take the length of the hypotenuse to be "m" and the length of the legs to be "h" and "k" then:

`h^2+k^2=m^2`

So, according to the problem, we have a right triangle and the values of both legs. Therefore it is possible to determine the hypotenuse:

h=4 in

k=6 in

`(4)^2+(6)^2=m^2\\16+36=m^2\\m^2=52\\m=√(52)\\m=√(4*13) \\m=2√(13)`

Finally, the length of the hypotenuse in inches is C.
`2√(13)`
`in^2`.