Respuesta :

Answer:

13 cm

Step-by-step explanation:

Use Pythagora's theorem to solve for the hypotenuse of the triangle:

[tex]a^2+b^2=c^2[/tex]

Where a and b are the two shorter legs, and c is the hypotenuse.

Replace the values in and solve for c:

[tex]5^2+12^2=c^2\\25+144=c^2\\169=c^2\\13=c[/tex]

AadhPrit

Answer:

The length of missing side of triangle is 13 cm.

Step-by-step explanation:

Solution :

Here, we have given that the two sides of triangle are 5 cm and 12 cm.

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 = 5 cm
  • [tex]\pink\star[/tex] b = 12 cm
  • [tex]\pink\star[/tex] c = ?

Substituting all the given values in the formula to find the third side of triangle :

[tex]\begin{gathered}\qquad{\longrightarrow{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = {(5)}^{2} + {(12)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = {(5 \times 5)} + {(12 \times 12)}}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = {(25)} + {(144)}}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = 25 + 144}}}\\\\\qquad{\longrightarrow{\sf{{(c)}^{2} = 169}}}\\\\\qquad{\longrightarrow{\sf{c= \sqrt{169}}}}\\\\\qquad{\longrightarrow{\sf{c= \sqrt{13 \times 13}}}}\\\\\qquad{\longrightarrow{\sf{c= 13 \: cm}}}\\\\ \qquad\star{\underline{\boxed{\sf{\red{c= 13 \: cm}}}}}\end{gathered}[/tex]

Hence, the length of missing side is 13 cm.

[tex]\rule{300}{2.5}[/tex]