Question

Найдите периметр прямоугольника если его площадь равна 54, а отношение соседних сторон равно 2:3

Answer 1

S=a*b стороны относятся как 2:3, значит a=2x , b = 3x S=2x*3x=6x^2=54 x^2=9 x1=3,   x2=-3 <0  отбрасываем Р=2(а+б) = 2(2х+3х)=2*5х=10х=10*3=30 см

Answer 2

Perimeter of a Rectangle with Given Area and Ratio of Sides

To find the perimeter of a rectangle when its area is 54 and the ratio of its adjacent sides is 2:3, we can follow these steps:

1. Let's assume the length of the rectangle is 2x and the width is 3x, based on the given ratio of 2:3. 2. The area of a rectangle is given by the formula: Area = length × width. In this case, the area is given as 54. So, we can write the equation as: 54 = (2x) × (3x). 3. Simplifying the equation, we get: 54 = 6x^2. 4. Dividing both sides of the equation by 6, we get: 9 = x^2. 5. Taking the square root of both sides, we find: x = 3. 6. Now that we know the value of x, we can find the length and width of the rectangle. The length is 2x, which is 2 × 3 = 6, and the width is 3x, which is 3 × 3 = 9. 7. The perimeter of a rectangle is given by the formula: Perimeter = 2 × (length + width). Substituting the values, we get: Perimeter = 2 × (6 + 9) = 2 × 15 = 30.

Therefore, the perimeter of the rectangle is 30.