The bases of the rectangular trapezoid are 14 and 24 cm, and the large diagonal is the bisectrix

| September 20, 2021 | education

The bases of the rectangular trapezoid are 14 and 24 cm, and the large diagonal is the bisectrix of the right angle. Find the perimeter of the trapezoid.

1. Vertices of the trapezoid A, B, C, D. BC = 14 units. AD = 24 units.

∠А = ∠В = 90 °. BD is the diagonal.

2. According to the problem statement, the diagonal BD is the bisector of the right angle, that is, it divides it into two equal angles.

Therefore, ∠ВАD = ∠В: 2 = 90 °: 2 = 45 °.

3.∠ВDD = 180 ° – 90 ° – 45 ° = 45 °.

4. The angles at the base BD of triangle ABD are equal. Therefore, the indicated triangle is isosceles. That is, AB = AD = 24 units.

5. From the top of C we draw the height CH.

CH = AB = 24 units.

BC = AH = 14 units.

6. DH = 24 – 14 = 10 units of measurement.

7. Calculate the length of the CD – the side of the trapezoid. For the calculation, we use the theorem

Pythagoras:

СD = √СН² + DH² = √24² + 10² = √576 + 100 = √676 = 26 units.

8. Calculate the perimeter (P) of a given trapezoid:

P = 26 + 24 + 14 + 24 = 88 units.

Answer: the perimeter of a given trapezoid is 88 units.



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