The hypotenuse of a right-angled triangle is 10 cm and the projection of the smaller leg onto the hypotenuse

| May 11, 2021 | education

The hypotenuse of a right-angled triangle is 10 cm and the projection of the smaller leg onto the hypotenuse is 3.6 cm, which is equal to the area of this triangle expressed in cm2.

Let ABC be a given right-angled triangle (angle C = 90 °). AB = 10 cm, BC is less than AC.

We omit the height CH (H belongs to AB), ВН is the projection of the BC leg onto the hypotenuse, BH = 3.6 cm.

Let’s find the length АН:

AB = AH + BH; AH = AB – BH = 10 – 3.6 = 6.4 (cm).

By the property of the height of a right-angled triangle, we calculate the length of CH.

CH = √ (AH * BH) = √ (6.4 * 3.6) = √23.04 = 4.8 (cm).

The area of a triangle is equal to half the product of the base and the height drawn to the base:

S = 1/2 * AB * CH = 1/2 * 10 * 4.8 = 5 * 4.8 = 24 (cm²).

Answer: the area of the triangle is 24 cm².



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.