Question

C одной и к прямой проведены перпендикуляр и 2 наклонные Найти длину перепендикуляра если длина наклонных 41см и 50 см а их проекции на данную прямую относятся как 3 к 10.

Answer 1

Может очень длинно, но проще не знаю

Answer 2

Problem Analysis

To solve this problem, we need to find the length of the perpendicular drawn to a given line when the lengths of the inclined lines and their projections on the given line are known. The given information is: - Length of the inclined lines: 41 cm and 50 cm - The ratio of their projections on the given line: 3:10

Solution

Let's denote the length of the perpendicular as x, the length of the inclined line as a, and the length of the projection on the given line as b. We know that the ratio of the projections on the given line is 3:10, so we can express the lengths of the projections as 3k and 10k, where k is a constant.

Using the given information, we can set up the following equation: a:b = 41:50 = 3k:10k

Calculation

To find the value of k, we can solve the equation: 41/3k = 50/10k

Solving for k: 41/3k = 50/10k 410k = 150k 410 = 150 k = 150/410

Now that we have the value of k, we can find the length of the perpendicular, x: x = √(41^2 - (3k)^2) = √(50^2 - (10k)^2)

Substitute the value of k into the equation to find x.

Final Answer

The length of the perpendicular is x cm.