The height of a right-angled triangle divides the hypotenuse into segments 18cm and 32cm long. Find the area of a triangle?

Let the value of the angle DАС of the triangle ABC be equal to X0, then the angle АСD = (90 – X) 0.

Angle ACB = 90, then angle BCD = (90 – (90 – X) = X0.

The acute angles of the right-angled triangles ACD and BCD are equal, then the triangles are similar in acute angle.

Then in similar triangles AD / CD = CD / BD.

CD ^ 2 = AD * BD = 32 * 18 = 576.

CD = 24 cm.

The length of the hypotenuse AB = AD + BD = 32 + 18 = 40 cm.

Determine the area of the triangle ABC.

Savs = AB * CD / 2 = 40 * 24/2 = 480 cm2.

Answer: The area of the triangle is 480 cm2.