The length of the oblique drawn from a point at a distance of 8 cm from the plane is 4 cm

The length of the oblique drawn from a point at a distance of 8 cm from the plane is 4 cm greater than the length of its projection onto this plane. Find the length of the slant.

The distance from point A to the plane is the perpendicular AB = 8 cm.

The segment BC is the projection of the inclined AC onto the plane, BC belongs to the plane, and therefore is perpendicular to AB.

Then triangle ABC is rectangular with right angle B.

Let the length of the leg BC = X cm, then the hypotenuse AC = (X + 4) cm.

Then, by the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2.

(X + 4) ^ 2 = X ^ 2 + 64.

X ^ 2 + 8 * X + 16 = X ^ 2 + 64.

8 * X = 48.

X = BC = 48/8 = 6 cm.

Then AC = 6 + 4 = 10 cm.

Answer: The length of the slope is 10 cm.