Question

Основанием прямой призмы является прямоугольник со сторонами 5 и 12 см диагональ призмы равна 17 см Найдите боковое ребро призмы

Answer 1

Диагональ основания=v(5^2+12^2)=v(25+144)=v169=13 см
боковое ребро=v(17^2-13^2)=v(289-169)=v120=2v30 см

Answer 2

Finding the Length of the Prism's Lateral Edge

To find the length of the lateral edge of the prism, we can use the Pythagorean theorem. The lateral edge is the hypotenuse of a right triangle formed by the prism's diagonal and one of its sides.

Given: - Length of one side of the prism: 5 cm - Length of another side of the prism: 12 cm - Length of the prism's diagonal: 17 cm

Let's denote the length of the lateral edge as x.

Using the Pythagorean theorem, we have:

x^2 = 5^2 + 12^2

Simplifying the equation:

x^2 = 25 + 144

x^2 = 169

Taking the square root of both sides:

x = √169

x = 13 cm

Therefore, the length of the lateral edge of the prism is 13 cm.