Question

через центр о вписаного в рівнобічну трапецію периметр якої дорівнює 52 см а менша основа 8 см до площини трапеції проведено перпендикуляр ОN.Довжина перпендикуляра проведеного із точки Nдо бічної сторони цієї трпеції дорівнює корінь 85см.Знайдіть довжину перпендикуляра ОN .Помогите пожалуйста

Answer 1

Пошаговое объяснение:

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Answer 2

Problem Analysis

To solve this problem, we need to find the length of the perpendicular ON drawn from point N to the lateral side of the trapezoid.

Given Information

- Perimeter of the trapezoid = 52 cm - Length of the smaller base = 8 cm - Length of the perpendicular ON = √85 cm

Solution

Let's denote the length of the larger base of the trapezoid as b, the height of the trapezoid as h, and the length of the perpendicular ON as x.

The perimeter of a trapezoid is given by the formula: Perimeter = Sum of all sides = a + b + c + d

Where a and c are the lengths of the parallel sides, and b and d are the lengths of the non-parallel sides.

In this case, we have: a + b + c + d = 52 cm

The length of the smaller base is given as 8 cm, so we can express the perimeter in terms of the smaller base and the unknown larger base: 8 + b + 8 + d = 52 b + d = 52 - 16 b + d = 36

We also know that the length of the perpendicular ON is √85 cm.

Using the properties of a trapezoid, we can express the area of the trapezoid in terms of the height (h), the smaller base (8), and the larger base (b): Area = (1/2) * (sum of bases) * height Area = (1/2) * (8 + b) * h

We can also express the area in terms of the length of the perpendicular ON (x): Area = (1/2) * (sum of parallel sides) * x Area = (1/2) * (8 + b + 8 + b) * x Area = (1/2) * (16 + 2b) * x

Equating the two expressions for the area, we get: (1/2) * (8 + b) * h = (1/2) * (16 + 2b) * x 8h + bx = 16x + 2bx 8h = 16x x = (8h) / 16 x = h / 2

So, the length of the perpendicular ON is half the height of the trapezoid.

Answer

The length of the perpendicular ON is half the height of the trapezoid.