Answer:
The value of x is 7.
Step-by-step explanation:
Solution :
Here, we have given that the two sides of triangle are 24 and 25.
Finding the third side of triangle by pythagoras theorem formula :
[tex]{\longrightarrow{\pmb{\sf{{(BC)}^{2} = {(AB)}^{2} + {(AC)}^{2}}}}}[/tex]
- [tex]\pink\star[/tex] BC = 25
- [tex]\pink\star[/tex] AB = 24
- [tex]\pink\star[/tex] AC = x
Substituting all the given values in the formula to find the third side of triangle :
[tex]{\longrightarrow{\sf{{(BC)}^{2} = {(AB)}^{2} + {(AC)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{{(25)}^{2} = {(24)}^{2} + {(x)}^{2}}}}[/tex]
[tex]{\longrightarrow{\sf{{(x)}^{2} = {(25)}^{2} - {(24)}^{2} }}}[/tex]
[tex]{\longrightarrow{\sf{{(x)}^{2} = {(25 \times 25)}- {(24 \times 24)} }}}[/tex]
[tex]{\longrightarrow{\sf{{(x)}^{2} = {(625)}- {(576)} }}}[/tex]
[tex]{\longrightarrow{\sf{{(x)}^{2} = 625 - 576 }}}[/tex]
[tex]{\longrightarrow{\sf{{(x)}^{2} = 625 - 576 }}}[/tex]
[tex]{\longrightarrow{\sf{{(x)}^{2} = 49}}}[/tex]
[tex]{\longrightarrow{\sf{(x)= \sqrt{49} }}}[/tex]
[tex]{\longrightarrow{\sf{(x)= 7}}}[/tex]
[tex]{\longrightarrow{\underline{\boxed{\sf{\purple{X= 7}}}}}}[/tex]
Hence, the value of x is 7.
[tex]\rule{300}{2.5}[/tex]
