Question

Полусумма оснований трапеции равна 6 , а разность оснований равна 4 . Найдите больше оснований

Answer 1

А - большее основание. 
b - меньшее основание

(a+b)/2=6
a+b=12
выразим а

a=12-b

а-b=4
12-b-b=4
-2b=-8
b=4
a=12-4=8

Ответ: 8

Answer 2

Solution for Finding the Length of the Other Base of a Trapezoid

To find the length of the other base of a trapezoid when the sum of the bases is 6 and the difference of the bases is 4, we can use the following approach:

1. Identify the Given Information: - The sum of the bases of the trapezoid is 6. - The difference of the bases of the trapezoid is 4.

2. Use the Formulas for the Sum and Difference of the Bases: - Let's denote the lengths of the two bases as \( b_1 \) and \( b_2 \). - The sum of the bases is given by \( b_1 + b_2 = 6 \). - The difference of the bases is given by \( |b_1 - b_2| = 4 \).

3. Solve for the Length of the Other Base: - We can solve the system of equations formed by the sum and difference of the bases to find the lengths of the bases.

- Adding the two equations, we get: \[ b_1 + b_2 + |b_1 - b_2| = 6 + 4 \] \[ 2b_1 = 10 \] \[ b_1 = 5 \]

- Subtracting the second equation from the first, we get: \[ b_1 - b_2 = 4 \] \[ 5 - b_2 = 4 \] \[ b_2 = 5 - 4 \] \[ b_2 = 1 \]

4. Conclusion: - The length of the other base of the trapezoid is 1.

This solution demonstrates that when the sum of the bases of a trapezoid is 6 and the difference of the bases is 4, the length of the other base is 1.