Given: ABCD – rectangular trapezoid. angle ACD = 90 degrees, AC = 60 cm, BC = 36 cm. find AD-?

| April 28, 2021 | education

From the top of the obtuse angle C, draw the height CH.

Quadrangle ABCH is a rectangle, since BC is parallel to AH as the base of the trapezoid, AB is parallel to CH as perpendiculars to the bases of the trapezoid, then BC = AH = 36 cm.

In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the leg CH.

CH ^ 2 = AC ^ 2 – AH ^ 2 = 60 ^ 2 – 36 ^ 2 = 3600 – 1296 = 2308.

CH = 48 cm.

According to the condition, the angle ACD = 90, then the height CH in it is drawn from a right angle, which means it is equal to the root of the square product of the segments by which the height divides the base AD.

CH = √AH * DH.

48 = √36 * DH.

√DH = 48/6 = 8.

DН = 64 cm.

Determine the length of the base AD.

AD = AH + DH = 36 + 64 = 100 cm.

Answer: The length of the base AD is 100 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.