Question

Средняя линия трапеции равна 7см. одно из ее оснований больше другого на 4 см.найдите основание трапеции

Answer 1

СРЕДНЯЯ ЛИНИЯ ТРАПЕЦИИ РАВНА ПОЛУСУММЕ ОСНОВАНИЙ
ОДНО ОСНОВАНИЕ=Х
ЗНАЧИТ
Х+(Х+4)=7*2
2Х=10
Х=5
ОТВЕТ  ОДНА СТОРОНА 5
ДРУГАЯ 5+4=9

Answer 2

Finding the Base of a Trapezoid

To find the base of a trapezoid, we need to use the given information about the trapezoid's average line and the difference between its bases.

Let's denote the length of the shorter base as x and the length of the longer base as x + 4 (since one base is 4 cm longer than the other).

The average line of a trapezoid is the line segment that connects the midpoints of the two bases. In this case, the average line is given as 7 cm.

To find the length of the average line, we can use the formula:

Average line = (length of shorter base + length of longer base) / 2

Substituting the given values, we have:

7 = (x + (x + 4)) / 2

Simplifying the equation, we get:

7 = (2x + 4) / 2

Multiplying both sides of the equation by 2, we have:

14 = 2x + 4

Subtracting 4 from both sides of the equation, we get:

10 = 2x

Dividing both sides of the equation by 2, we have:

x = 5

Therefore, the length of the shorter base is 5 cm.

To find the length of the longer base, we can substitute the value of x into the expression x + 4:

Length of longer base = 5 + 4 = 9 cm

So, the length of the longer base is 9 cm.

Therefore, the bases of the trapezoid are 5 cm and 9 cm.