From a point to a straight line, two oblique ones are drawn, the projection lengths of which are 12 and 30 cm.

From a point to a straight line, two oblique ones are drawn, the projection lengths of which are 12 and 30 cm. Find the oblique lengths if they relate as 10:17.

Let the lesser of the oblique be equal to the expression 10m.

Then, in accordance with the condition, another oblique can be written as 17m.

Since, by condition, we know the lengths of their projection, it is possible to write down an equality, the parts of which will be two equations according to the Pythagorean theorem:

(10m) ^ 2 – 12 ^ 2 = (17m) ^ 2 – 30 ^ 2;

100m ^ 2 – 144 = 289m ^ 2 – 900;

189m ^ 2 = 756;

m2 = 4;

m1 = 2;

m2 = -2 (does not match the condition);

2 * 10 = 20;

2 * 17 = 34.

Answer: The first slope is 20 cm, and the second slope is 34 cm.