Question

В прямоугольном параллелепипеде длины сторон основания относятся как 7:24, а площадь диагонального сечения равна 50 дм2 . Найдите площадь боковой поверхности

Answer 1

Площадь боковой поверхности параллелепипеда равна P*h, где Р - периметр основания, h - выоста параллелепипеда. Пусть стороны основания 7х и 24х. Тогда Sбок = 2*(7x+24x)*h=

=62 x h.

Диагональ основания по теореме Пифагора равна d = корень квадратный (49x^2  +  576x^2) =

=корень625 x^2=25 x.

Площадь диагонального сечения равна  d*h  = 25 x h = 50. Значит, x h = 50:25=2

Следовательно,  S бок = 62 * 2 = 124

Answer 2

Solution for Finding the Surface Area of the Rectangular Parallelepiped

To find the surface area of the rectangular parallelepiped, we can use the given information about the ratio of the sides of the base and the area of the diagonal section.

Given: - Ratio of the sides of the base: 7:24 - Area of the diagonal section: 50 dm^2

Calculating the Surface Area of the Rectangular Parallelepiped

First, let's find the dimensions of the base of the parallelepiped. Let's assume the sides of the base are 7x and 24x, where x is a common factor.

The area of the diagonal section can be expressed in terms of the sides of the base using the Pythagorean theorem. The formula for the area of the diagonal section is given by:

Area of diagonal section = (side1)^2 + (side2)^2

Substituting the given values: 50 = (7x)^2 + (24x)^2

Solving for x: 50 = 49x^2 + 576x^2 50 = 625x^2 x^2 = 50 / 625 x^2 = 0.08 x = √0.08 x ≈ 0.2828

Now that we have the value of x, we can find the dimensions of the base: Side1 = 7x ≈ 7 * 0.2828 ≈ 1.98 dm Side2 = 24x ≈ 24 * 0.2828 ≈ 6.77 dm

The dimensions of the base are approximately 1.98 dm and 6.77 dm.

Calculating the Surface Area

The surface area of the rectangular parallelepiped can be calculated using the formula: Surface Area = 2 * (length * width + width * height + height * length)

Substituting the values: Surface Area = 2 * (1.98 * 6.77 + 6.77 * 7 + 7 * 1.98) Surface Area ≈ 2 * (13.3946 + 47.39 + 13.86) Surface Area ≈ 2 * 74.6446 Surface Area ≈ 149.2892 dm^2

Therefore, the approximate surface area of the rectangular parallelepiped is 149.2892 dm^2.