If in a rectangular trapezoid the smaller side is 12 cm, the smaller diagonal is perpendicular to the larger

| February 4, 2021 | education

If in a rectangular trapezoid the smaller side is 12 cm, the smaller diagonal is perpendicular to the larger side and is 15 cm, which is the length of the larger base.

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

BC ^ 2 = AC ^ 2 – AB ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81.

BC = 9 cm.

Let us draw the height of CH from the top of the obtuse angle. Quadrangle ABCН is a rectangle, then CH = AB = 12 cm, AH = BC = 9 cm.

By condition the AСD triangle is rectangular. Then the height of the CH divides the hypotenuse of the BP into two segments, the square root of the product of which is equal to the length of the height of the CH.

CH = √AН * DН.

12 = √9 * DН.

√DН = 12/3 = 4 cm.

DН = 16 cm.

Determine the length of the base of the blood pressure.

AD = AН + DН= 9 + 16 = 25 cm.

Answer: The length of the larger base is 25 cm.



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