Question

They hypotenuse of a right triangle is 26 feet long. One leg of the trisangle is 14 feet longer than the other leg find the length of the legs of the triangle

Answer 1

We have:
c = 26 ft - a hypotenusea - a lega + 14 - a leg
Use the Pythagorean theorem:
$a^2+(a+14)^2=26^2$
Use: (a + b)² = a² + 2ab + b²
$a^2+a^2+28a+196=676\ \ \ |-676\\\\2a^2+28a-480=0\ \ \ |:2\\\\a^2+14a-240=0\\\\a^2+24a-10a-240=0\\\\a(a+24)-10(a+24)=0\\\\(a+24)(a-10)=0\iff a+24=0\ \vee\ a-10=0\\\\a=-24 < 0\ \vee\ a=10$
Answer: 10 ft and 24 ft.