Question

З точки до площини проведені дві похилі, одна з них на 7 см менша за другу. Проекції похилих дорівнюють 5 см і 16 см. Знайти похилі.

Answer 1

Ответ:

13 см и 20 см

Объяснение:

DB⊥ α

DA - похіла, АВ - проекція DA на площину α

DС - похіла, ВС - проекція DС на площину α

ΔАDB та ΔСDB - прямокутні

Хай гіпотенуза DС = х см, тоді АD= (х+7) см

За теоремою Піфагора маємо:

DB² = DС²-ВС² = х²-5² - з прямокутного ΔСDB

DB² = АD² - АВ² = (х+7)²-16² - з прямокутного ΔАDB

х²-5² = (х+7)²-16²

х² - 25 = х² + 14х+49-256

14х= 182

х=13

DС = 13 см, АD = 13+7 = 20см

Answer 2

Ответ:

13 см,  20 см.

Объяснение:

ΔАОВ та ΔАОС - прямокутні;  ОВ=5 см,  ОС=16 см.

Нехай АВ=х см,  тоді  АС=х+7 см

За теоремою Піфагора

АО²=АВ²-ОВ²  і АО²=АС²-ОС²  тобто АВ²-ОВ²=АС²-ОС²

х²-25=(х+7)²-256

х²-25=х²+14х+49-256

14х=182;  х=13

АВ=13 см,  АС=13+7=20 см.

Answer 3

Problem Analysis

We are given two inclined lines and their projections on a plane. One of the inclined lines is 7 cm shorter than the other, and the projections of the inclined lines on the plane are 5 cm and 16 cm. We need to find the lengths of the inclined lines.

Solution

Let's assume the lengths of the inclined lines are x cm and x - 7 cm, respectively.

According to the problem, the projections of the inclined lines on the plane are 5 cm and 16 cm. We can use the concept of similar triangles to solve this problem.

The ratio of the lengths of the projections to the lengths of the inclined lines will be the same for both inclined lines. Therefore, we can set up the following equation:

5 / x = 16 / (x - 7)

To solve this equation, we can cross-multiply:

5(x - 7) = 16x

Simplifying the equation:

5x - 35 = 16x

Bringing the variables to one side:

16x - 5x = 35

11x = 35

Dividing both sides by 11:

x = 35 / 11

Calculating the value of x:

x ≈ 3.18

Therefore, the length of the longer inclined line is approximately 3.18 cm, and the length of the shorter inclined line is approximately 3.18 - 7 = -3.82 cm.

However, it is not possible to have a negative length for a line segment, so we can conclude that there is no solution to this problem.

Conclusion

The lengths of the inclined lines cannot be determined based on the given information.