Question

The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth. 10.2 inches 24.0 inches 28.2 inches 30.0 inches

Answer 1

10.2

Explanation:

is a pimp ting

Answer 2

10.2 inches

Explanation:

we know that

In this problem we have two cases

First case

The given lengths are two legs of the right triangle

so

`a=12\ in, b=15\ in`

Applying the Pythagoras Theorem

Find the length of the hypotenuse

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

substitute

`c^(2)=12^(2) +15^(2)`

`c^(2)=369`

`c=19.2\ in`

Second case

The given lengths are one leg and the hypotenuse

so

`a=12\ in, c=15\ in`

Applying the Pythagoras Theorem

Find the length of the other leg

`b^(2)=c^(2) - a^(2)`

substitute

`b^(2)=15^(2) - 12^(2)`

`b^(2)=81`

`b=9\ in`

Find the difference between the two possible lengths of the third side of the triangle

so

`19.2-9=10.2\ in`