Question

Помогитееееее Знайдіть сторони прямокутника якщо його периметр дорівнює 24 см а площа 32 см2

Answer 1

Cтороны прямоугольника х и y ( cм )
Система уравнений 
2( x + y ) = 24 
xy = 32 
x > 0 ; y > 0 
Решение 
x + y = 24 : 2 
x = 12 - y 
y( 12 - y ) = 32 
12y - y² = 32 
y² - 12y + 32 = 0 
D = 144 - 128 = 16 = 4²
y1 = ( 12 + 4 ) : 2 = 8 
y2 = ( 12 - 4 ) : 2 = 4 
x1 = 12 - 8 = 4 
x2 = 12 - 4 = 8 
Ответ 4 см и 8 см ( или 8 см и 4 см ) 

Answer 2

Finding the Sides of a Rectangle

To find the sides of a rectangle given its perimeter and area, we can use the following formulas:

1. Perimeter of a rectangle: P = 2(l + w), where P is the perimeter, l is the length, and w is the width. 2. Area of a rectangle: A = l * w, where A is the area, l is the length, and w is the width.

In this case, we are given that the perimeter of the rectangle is 24 cm and the area is 32 cm². Let's use these values to find the sides of the rectangle.

Solution

1. Perimeter: We are given that the perimeter of the rectangle is 24 cm. Using the formula for the perimeter, we can set up the equation: 24 = 2(l + w)

2. Area: We are given that the area of the rectangle is 32 cm². Using the formula for the area, we can set up the equation: 32 = l * w

To solve these equations, we can use substitution or elimination. Let's use substitution:

From the first equation, we can express one variable in terms of the other. Let's solve for l: l = (24 - 2w) / 2

Now, substitute this value of l into the second equation: 32 = [(24 - 2w) / 2] * w

Simplifying the equation: 64 = 24w - 2w²

Rearranging the equation: 2w² - 24w + 64 = 0

Now, we can solve this quadratic equation to find the values of w. We can use the quadratic formula: w = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 2, b = -24, and c = 64. Substituting these values into the quadratic formula, we get: w = (-(-24) ± √((-24)² - 4 * 2 * 64)) / (2 * 2)

Simplifying further: w = (24 ± √(576 - 512)) / 4 w = (24 ± √64) / 4 w = (24 ± 8) / 4

This gives us two possible values for w: 1. w = (24 + 8) / 4 = 32 / 4 = 8 cm 2. w = (24 - 8) / 4 = 16 / 4 = 4 cm

Now, substitute these values of w back into the equation for l: 1. l = (24 - 2 * 8) / 2 = (24 - 16) / 2 = 8 / 2 = 4 cm 2. l = (24 - 2 * 4) / 2 = (24 - 8) / 2 = 16 / 2 = 8 cm

Therefore, the sides of the rectangle are: 1. Length = 8 cm, Width = 4 cm 2. Length = 4 cm, Width = 8 cm

Answer

The sides of the rectangle can be either 8 cm by 4 cm or 4 cm by 8 cm, depending on the orientation of the rectangle.