Question

трапеція вписано в коло так , що діаметр кола є більшою основою трапеції,а менша основна дорівнює бічній стороні.знайдіть основи трапеції,якщо її периметр дорівнює 20см

Answer 1

To find the bases of the trapezoid, we need to use the given information that the diameter of the circle is larger than the larger base of the trapezoid, and the smaller base is equal to the lateral side. We also know that the perimeter of the trapezoid is 20 cm.

Let's denote the larger base as b1, the smaller base as b2, and the lateral side as a.

Formulas for the Perimeter of a Trapezoid:

The perimeter of a trapezoid can be calculated using the formula: Perimeter = b1 + b2 + 2a.

Given that the perimeter is 20 cm, we can write the equation as: 20 = b1 + b2 + 2a. [[1]]

Relationship between the Diameter of the Circle and the Bases of the Trapezoid:

We are given that the diameter of the circle is larger than the larger base of the trapezoid. Let's denote the diameter as d.

Since the diameter of the circle is larger than the larger base, we can write the inequality: d > b1.

Solving for the Bases of the Trapezoid:

To find the bases of the trapezoid, we need to solve the system of equations formed by the perimeter equation and the inequality equation.

Let's substitute d for b1 in the perimeter equation: 20 = d + b2 + 2a.

Now we have two equations: 20 = d + b2 + 2a [[1]] d > b1.

Since we don't have the value of d, we cannot solve the system of equations without additional information. Please provide the value of d or any other relevant information to proceed with the calculation.

If you have any further questions, feel free to ask!