Question

Разность основания трапеции 8 см средняя линия равна 16 см . найти основание

Answer 1

X-y=8
x+y=32

решим систему 
x=8+y
8+2y=32
2y=24
y=12
x=20

то есть основания равны 12 и  20

Answer 2

Finding the Base of a Trapezoid

To find the base of a trapezoid when the difference between the bases is 8 cm and the length of the median is 16 cm, we can use the formula for the area of a trapezoid.

The formula for the area of a trapezoid is given by:

Area = (1/2) * (sum of the bases) * height

In this case, the median of the trapezoid is equal to the average of the bases. Let's assume the length of the shorter base is x cm. Then, the length of the longer base would be (x + 8) cm.

Given that the length of the median is 16 cm, we can set up the following equation:

16 = (x + (x + 8))/2

Simplifying the equation:

16 = (2x + 8)/2

Multiplying both sides of the equation by 2:

32 = 2x + 8

Subtracting 8 from both sides:

24 = 2x

Dividing both sides by 2:

x = 12

Therefore, the length of the shorter base is 12 cm, and the length of the longer base is (12 + 8) cm, which is equal to 20 cm.

So, the base of the trapezoid is 12 cm.