In a right-angled triangle, one leg is 3 longer than the other, and the area is 18. Find the length of the hypotenuse.

univerkov | September 8, 2021 | education

Let the length of the leg BC = X cm, then, by condition, the length of the leg AB = (X + 3) cm.

The area of the triangle is equal to: Savs = AB * BC / 2.

18 = (X +3) * X / 2.

X ^ 2 + 3 * X – 36 = 0.

Let’s solve the quadratic equation.

X = BC = (3/2) * √17 – 3/2 cm.

AB = (3/2) * √17 + 3/2 cm.

By the theorem of Pmfagor, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = ((3/2) * √17 – 3/2) ^ 2 + ((3/2) * √17 + 3/2) ^ 2 = (153/4 – (18/4) * √17 + (9/4) + (153/4 + (18/4) * √17 + (9/4) = 324/4 = 81.

AC = 9 cm.

Answer: The length of the hypotenuse is 9 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.