Question

В прямоугольном параллелепипеде боковое ребро равно 5 см площадь диагонального сечения 205 см а плащадь основания 360 см Определите стороны основания паралелипипеда

Answer 1

Пусть стороны основания х-длина и у-ширина,
тогда S основания=х*у=360 см ^2 
диагональ основания =корень из (х^2+y^2),
 тогда S диагонального сечения = корень из (х^2*y^2) * 5 = 205 см кв., тогда корень из(х^2+y^2) = 41(х^2+y^2)=1681,    
 выразим х из выражения х*у=360, получим х=360/у,
подставим((360/у)^2+y^2)=1681(129600/y^2)+y^2=1681, 
заменим у^2 на а, тогда получим :129600/а + а =1681,
домножим на а, чтобы избавиться от дробей, получим:
129600+а^2=1681aa^2-1681a+129600=0D=2825761-4*129600=2825761-518400=2307361a1=(1519-1681)/2= отрицательное число,
 не удовлетворяющее условию, а2=(1519+1681)/2=1600,
значит у^2=1600, тогда у=корень из 1600у=40 см, тогда х*40=360х=360/40х=90 см 
Ответ: Стороны основания 40 и 90 сантиметров. 
Примерно так  :-)

Answer 2

Calculation of the Base Sides of the Rectangular Parallelepiped

To determine the sides of the base of the rectangular parallelepiped, we can use the given information about the lateral edge, the area of the diagonal section, and the area of the base.

Let's denote the sides of the base as a and b.

We know that the lateral edge of the parallelepiped is 5 cm. This means that the diagonal of the base is also 5 cm.

The area of the diagonal section is given as 205 cm². Since the diagonal of the base is 5 cm, we can use the formula for the area of a rectangle to find the product of the sides of the base:

a * b = 205 cm² [[1]]

We are also given that the area of the base is 360 cm². Therefore, we have:

a * b = 360 cm² [[2]]

Now we have a system of equations:

a * b = 205 cm² [[1]]

a * b = 360 cm² [[2]]

To solve this system, we can use substitution. From equation [[2]], we can express a in terms of b:

a = 360 / b [[3]]

Substituting equation [[3]] into equation [[1]], we get:

(360 / b) * b = 205

Simplifying the equation:

360 = 205 * b

Solving for b:

b = 360 / 205

Calculating the value of b:

b ≈ 1.7561

Substituting the value of b back into equation [[3]], we can find a:

a = 360 / 1.7561

Calculating the value of a:

a ≈ 205.7143

Therefore, the sides of the base of the parallelepiped are approximately 205.7143 cm and 1.7561 cm.

Please note that these values are approximations due to rounding.

Let me know if there's anything else I can help you with!