Question

Знайдіть основи трапеції, якщо вони відносяться як 3:5, а середня лінія дорівнює 24см. Менша основа.....- см, більша основа.....- см.​

Answer 1

Ответ:

Средняя линия трапеции-полусумма оснований
Сумма оснований

24•2=48 см

Меньшее основание 3Х

БОльшее основание 5Х

3Х+5Х=48 см

8Х=48

Х=48:8

Х=6

Меньшее основание

6•3=18 см

БОльшее основание

6•5=30 см

Объяснение:

Answer 2

Finding the Lengths of the Bases of a Trapezoid

To find the lengths of the bases of a trapezoid when the ratio of the bases is 3:5 and the median is 24 cm, we can use the following steps:

1. Understand the Relationship Between the Median and the Bases: - The median of a trapezoid is the line segment that joins the midpoints of the two non-parallel sides of the trapezoid.

2. Use the Median to Find the Average of the Bases: - The median of a trapezoid is equal to the average of the lengths of the two bases.

3. Apply the Given Ratio to Find the Lengths of the Bases: - Since the ratio of the bases is 3:5, we can use this ratio to find the lengths of the bases.

Calculating the Lengths of the Bases

Given: - Ratio of the bases: 3:5 - Median length: 24 cm

Let's denote the lengths of the smaller and larger bases as x and y respectively.

Using the given ratio, we can express the relationship between the lengths of the bases as: - x:y = 3:5

We also know that the median is equal to the average of the lengths of the bases: - (x + y) / 2 = 24

Solving for the Lengths of the Bases

To find the lengths of the bases, we can use the relationship between the bases and the median:

1. From the ratio x:y = 3:5, we can express one variable in terms of the other. Let's solve for y in terms of x: - y = (5/3)x

2. Substitute the expression for y into the equation for the median: - (x + (5/3)x) / 2 = 24 - (8/3)x / 2 = 24 - (4/3)x = 24 - x = 24 * (3/4) - x = 18

3. Now that we have the value of x, we can find the value of y using the ratio: - y = (5/3)*18 - y = 30

Conclusion

Therefore, the lengths of the bases are: - The smaller base: 18 cm - The larger base: 30 cm

Answer 3

Finding the Lengths of the Bases of a Trapezoid

To find the lengths of the bases of a trapezoid, we can use the given ratio and the length of the median line. Let's solve the problem step by step.

Given information: - The ratio of the bases is 3:5. - The length of the median line is 24 cm. - The length of the smaller base is unknown. - The length of the larger base is also unknown.

Let's assume the length of the smaller base is x cm. Since the ratio of the bases is 3:5, the length of the larger base can be represented as (5/3)x cm.

Now, we know that the median line of a trapezoid is the average of the lengths of the bases. In this case, the median line is given as 24 cm. So, we can set up the following equation:

((x + (5/3)x) / 2) = 24

Simplifying the equation, we get:

((8/3)x) / 2 = 24

Multiplying both sides by 2, we have:

(8/3)x = 48

To isolate x, we can multiply both sides by 3/8:

x = (3/8) * 48

Simplifying further, we find:

x = 18

Therefore, the length of the smaller base is 18 cm.

To find the length of the larger base, we can substitute the value of x into the expression (5/3)x:

Length of larger base = (5/3) * 18 = 30

Therefore, the length of the larger base is 30 cm.

In summary: - The length of the smaller base is 18 cm. - The length of the larger base is 30 cm.

Please let me know if there's anything else I can help you with!