Answer:
The length of b is 12 mm.
Step-by-step explanation:
Solution :
Here, we have given that the two sides of triangle are 9 mm and 15 mm.
Finding the third side of triangle by pythagoras theorem formula :
[tex]{\longrightarrow{\pmb{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}}[/tex]
- [tex]\pink\star[/tex] a = 9 mm
- [tex]\pink\star[/tex] c = 15 mm
- [tex]\pink\star[/tex] b = ?
Substituting all the given values in the formula to find the third side of triangle :
[tex]{\longrightarrow{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{{(15)}^{2} = {(9)}^{2} + {(b)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{{(15 \times 15)}= {(9 \times 9)}+ {(b)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{{(225)}= {(81)}+ {(b)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{225= 81+ {(b)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{{(b)}^{2} = 225 - 81}}}[/tex]
[tex]{\longrightarrow{\sf{{(b)}^{2} = 144}}}[/tex]
[tex]{\longrightarrow{\sf{b = \sqrt{144} }}}[/tex]
[tex]{\longrightarrow{\sf{b = 12}}}[/tex]
[tex]\star{\underline{\boxed{\sf{\purple{b = 12 \: mm}}}}}[/tex]
Hence, the length of b is 12 mm.
[tex]\rule{300}{2.5}[/tex]
