Question

В основі прямої призми лежить прямокутний трикутник із гіпотенузою 20 см і катетом 16 см. Знайти довжину діагоналі грані призми, що містить менший катет трикутника, якщо висота призми дорівнює 5 см. ДУЖЕ СРОЧНОО, ПЖ ДОПОМОЖІТЬ

Answer 1

Calculation of the Diagonal of the Prism

To find the length of the diagonal of the face of the prism that contains the smaller leg of the triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the smaller leg of the triangle is given as 16 cm, and the hypotenuse is given as 20 cm. Let's denote the length of the diagonal of the prism as d.

Using the Pythagorean theorem, we can set up the following equation:

d^2 = 16^2 + 20^2

Simplifying the equation:

d^2 = 256 + 400

d^2 = 656

Taking the square root of both sides to solve for d:

d = √656

Calculating the square root of 656, we find:

d ≈ 25.61 cm

Therefore, the length of the diagonal of the face of the prism that contains the smaller leg of the triangle is approximately 25.61 cm.

Please note that the search results provided by You.com did not directly answer the question. The calculation was performed using the Pythagorean theorem.