Answer:
The other leg of the triangle is 12.
Explanation:
Given:
Hypotenuse of triangle is 13 and a leg(Leg1) is 5.
Let, the other leg of the triangle (Leg2) be
.
Now, putting the formula:
![(Hypotenuse)^(2)=(Leg1)^(2)+(Leg2)^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/fx4b15etlx5q3v3z6rc441ksfkrnfgc73j.png)
⇒
![13^(2) =5^(2) +x^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/bg761node4ca2b7mlno0o8iu5z2fxz6jq0.png)
⇒
![169=25+x^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7qfzwvcvi4pfn9zoso236opi3wx6w5fyl0.png)
⇒
![169-25=x^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/3l983mq1ym4cng5pxkc7ekncv2r3yerllh.png)
⇒
![144=x^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/i7upgcz4fxc605dwdwlp8dt697cpgxfshw.png)
Taking square root both sides
⇒
![12=x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/mqfl0s9by5tq4dt8qlgh2snergn7smvwsi.png)
⇒
.
Therefore, the other leg of the triangle is 12.