The diagonal of a television screen is 50 cm, the length of its sides is 3: 4. What are the lengths of the sides of the screen?

The television screen is rectangular in shape.

Let the sides of the rectangle be a and b.

By the Pythagorean theorem, we obtain the dependence of the length of the diagonal on the lengths of the sides of the rectangle:

d ^ 2 = a ^ 2 + b ^ 2.

But according to the condition of the problem:

a / b = 3/4,

a = 3/4 * b. We have:

50 ^ 2 = 9/16 * b ^ 2 + b ^ 2 = 25/16 * b ^ 2,

50 = 5/4 * b,

b = 40.

Then:

a = 3/4 * b = 3/4 * 40 = 30.

Answer: the lengths of the sides of the screen are 40 cm and 30 cm.