Question

Одна з основ трапеції на 8 см більша за другу, а середня лінія дорівнює 17 см. Знайти більшу основу трапеції.

Answer 1

Нехай більша основа х см, тоді менша х-8 см. Середня лінія дорівнює напівсумі основ, тобто

17=(х+х-8)/2

2х-8=34

2х=42

х=21

Відповідь: 21 см.

Answer 2

Finding the larger base of a trapezoid

To find the larger base of a trapezoid, we can use the formula for the area of a trapezoid, which is given by:

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

In this case, we are given that the average line of the trapezoid is 17 cm. Let's assume that the smaller base is x cm. Since the larger base is 8 cm greater than the smaller base, we can express it as (x + 8) cm.

Now, we can set up the equation using the formula for the area of a trapezoid:

Area = (1/2) * (x + (x + 8)) * 17

Simplifying the equation:

Area = (1/2) * (2x + 8) * 17

Area = 17x + 68

Since we don't have the value of the area, we cannot solve for x directly. However, we can still find the larger base by substituting different values for x and calculating the corresponding area. The larger base will be the one that gives us the desired area.

Let's calculate the area for a few values of x:

- For x = 1 cm, the area is 17(1) + 68 = 85 square cm. - For x = 2 cm, the area is 17(2) + 68 = 102 square cm. - For x = 3 cm, the area is 17(3) + 68 = 119 square cm.

Based on these calculations, we can see that as x increases, the area also increases. Therefore, the larger base of the trapezoid will be the one that gives us the desired area.

Unfortunately, without the value of the area or any additional information, we cannot determine the exact value of the larger base of the trapezoid.