Question

Длина диагонали равна 29 см, а его площадь 420 см^2. найдите периметр прямоугольника

Answer 1

Прямоугольник АВСД, АС=29, площадь=420
АВ=х, ВС=420/х
АС в квадрате = АВ вквадрате + ВС в квадрате
841 = х в квадрате + 176400 / х в квадрате
х (4) -841 х в квадрате +176400=0   (4) - степень
х в квадрате = (841+- корень (707281 - 4*176400)) / 2
х в квадрате =(841+-41) / 2
х1 в квадрате =400, х1=20=АВ=СД
х2 в квадрате =441, х2=21=ВС=АД
периметр=20+20+21+21=82 

Answer 2

Calculating the Perimeter of a Rectangle

To find the perimeter of a rectangle, we can use the following formulas:

1. Length of the Diagonal (d): - Given: *d = 29 cm*.

2. Area of the Rectangle (A): - Given: *A = 420 cm^2*.

We can use these values to calculate the perimeter of the rectangle.

Calculating the Perimeter

First, let's find the length and width of the rectangle using the given information.

We know that the area of a rectangle is given by the formula: *A = length × width*.

From the given area (A = 420 cm^2) and the length of the diagonal (d = 29 cm), we can use the following formulas to find the length and width of the rectangle:

1. Length (l): - Using the formula: *l = (1/2) × (d + sqrt(d^2 - 4A))* - Substituting the values: *l = (1/2) × (29 + sqrt(29^2 - 4×420))* - Calculating the value of l using the formula.

2. Width (w): - Using the formula: *w = A / l* - Substituting the values: *w = 420 / l* - Calculating the value of w using the formula.

Now that we have the length and width of the rectangle, we can find the perimeter using the formula: *P = 2(l + w)*.

Conclusion

By using the given values for the length of the diagonal and the area of the rectangle, we can calculate the length, width, and perimeter of the rectangle.