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 :
![{\longrightarrow{\pmb{\sf{{(BC)}^(2) = {(AB)}^(2) + {(AC)}^(2)}}}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/t3wssuf9bzfflqakrory2050zdl7136h9e.png)
Substituting all the given values in the formula to find the third side of triangle :
![{\longrightarrow{\sf{{(BC)}^(2) = {(AB)}^(2) + {(AC)}^(2)}}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/8bmzuvp07dbh2usfxn1mali9hbyv0ia5yp.png)
![{\longrightarrow{\sf{{(25)}^(2) = {(24)}^(2) + {(x)}^(2)}}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/gtyvr3u6uxcahw0ratmev1waf3aciqt5rl.png)
![{\longrightarrow{\sf{{(x)}^(2) = {(25)}^(2) - {(24)}^(2) }}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/7olcy7wla31ep2q534gz231328y2hkcvzn.png)
![{\longrightarrow{\sf{{(x)}^(2) = {(25 * 25)}- {(24 * 24)} }}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/os63iqul8d8mtbl3s4h445v90doswael64.png)
![{\longrightarrow{\sf{{(x)}^(2) = {(625)}- {(576)} }}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/jqx899yloduey5x9c7e6cm3j1avl8vjroa.png)
![{\longrightarrow{\sf{{(x)}^(2) = 625 - 576 }}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/rive70xzzhimj46cys7h7n4dkrxc50j62s.png)
![{\longrightarrow{\sf{{(x)}^(2) = 625 - 576 }}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/rive70xzzhimj46cys7h7n4dkrxc50j62s.png)
![{\longrightarrow{\sf{{(x)}^(2) = 49}}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/go47aobyvfzdn05kk8galzlxjtvv84bmsr.png)
![{\longrightarrow{\sf{(x)= √(49) }}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/gvwqv5tsbmhhr7rwqinm4co8luom2h01mp.png)
![{\longrightarrow{\sf{(x)= 7}}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/hk9bpp0q21u711k4z7ilm1mhm4489k66b2.png)
![{\longrightarrow{\underline{\boxed{\sf{\purple{X= 7}}}}}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ci5dm4yl7shmb81bv4g49hox5b6xmfi3t5.png)
Hence, the value of x is 7.
![\rule{300}{2.5}](https://img.qammunity.org/2023/formulas/mathematics/high-school/4wr5wvuxv3n1yp1b1sykhxf527peu2ltxm.png)