Question

В прямой треугольной призме стороны основания ровны 6,8,10 ,площадь полной поверхности ровна 240 найдите высоту призмы

Answer 1

Решения в приложении

Answer 2

Calculation of the Prism's Height

To find the height of the prism, we can use the formula for the surface area of a rectangular prism, which is given by:

Surface Area = 2lw + 2lh + 2wh

In this case, the prism is a right triangular prism, so one of the sides of the base is the height of the prism. Let's denote the height of the prism as 'h'.

Given that the sides of the base are 6, 8, and 10, and the total surface area is 240, we can set up the equation as follows:

240 = 2(6)(8) + 2(6)(h) + 2(8)(h)

Simplifying the equation, we get:

240 = 96 + 12h + 16h

Combining like terms, we have:

240 = 96 + 28h

Subtracting 96 from both sides, we get:

144 = 28h

Finally, dividing both sides by 28, we find:

h = 5.14

Therefore, the height of the prism is approximately 5.14 units.