Find the corners of a parallelogram with an area of 24 cm2 if its height, drawn from the top, divides

Find the corners of a parallelogram with an area of 24 cm2 if its height, drawn from the top, divides the base of the parallelogram into 3 cm and 5 cm segments, counting from the top of the acute angle.

Find the base of the parallelogram. Its length is equal to the sum of the lengths of the segments into which the height drawn to it divides: a = 3 + 5 = 8 cm. The area of ​​the parallelogram is equal to the product of the height by the base S = a * h. Knowing the area of ​​the parallelogram and its base, we can find the height: h = S / a = 24/8 = 3 cm.
Consider a right-angled triangle formed by the height, the side of the parallelogram, and the smaller base segment (closest to the acute angle). In this triangle, the side of the parallelogram is the hypotenuse, and the height and the smaller segment are legs, each of which is 3 cm.Therefore, we have an isosceles right triangle in which the apex angle is 90 degrees. Since the sum of the angles of a triangle is 180, and the angles at the base of an isosceles triangle are equal, we find the value of the angles at the base: (180-90) / 2 = 90/2 = 45. Thus, the acute angle of the parallelogram is 45 degrees, and the adjacent obtuse angle is 180-45 = 135 degrees, because the sum of the adjacent angles of a parallelogram is 180 degrees.