Question

The two shorter sides of an obtuse triangle measure 15 inch and 3 ft describe the length of the longest side

Answer 1

The length of the longest side are all real numbers greater than 39 inches and less than 51 inches

Explanation:

we know that

In an obtuse triangle

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

where

c is the length of the longest side

a and b are the two shorter sides

Convert the dimensions in inches

`1\ ft=12\ in`

`3\ ft=3*12=36\ in`

substitute the values

`c^(2) >15^(2)+36^(2)`

`c^(2) >1,521`

`c >39 in`

Applying the triangle inequality Theorem

1)
`15+36 >c`

`c <51 in`

2)
`c+15 >36`

`c>21 in`

therefore

The length of the longest side belong to the interval
`(39,51)`

All real numbers greater than 39 inches and less than 51 inches