Question

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

Answer 1

Answer:

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

Step-by-step 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