Question

площа прямокутныка = 180см в квадрате,а його периметр=54см. знайти сторони прямокутника

Answer 1

 

S=a*b=180

P=2*(a+b)=54

a+b=27

 

 

 

 выразим а     а=27-b

и подставим в формулу площади

 

s=(27-b)*b

 

 

 

 

 

 

 27b-b^2=180

-b^2+27b-180=0

b^2-27b+180=0

теорема виэта

x1+x2=27

x1*x2=180

x1=15

x2=12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Calculation of Rectangle Sides

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

1. Area of a rectangle: Area = length × width 2. Perimeter of a rectangle: Perimeter = 2 × (length + width)

Let's solve the problem step by step.

Given: - Area of the rectangle = 180 cm² - Perimeter of the rectangle = 54 cm

Let's assume the length of the rectangle is L and the width is W.

Using the formulas mentioned above, we can set up the following equations:

1. Equation for the area: L × W = 180 2. Equation for the perimeter: 2 × (L + W) = 54

Now, let's solve these equations to find the values of L and W.

From the equation for the perimeter, we can simplify it to: L + W = 27 (dividing both sides by 2)

Next, we can solve this equation for one variable and substitute it into the equation for the area.

Let's solve for L: L = 27 - W

Substituting this value of L into the equation for the area: (27 - W) × W = 180

Expanding and rearranging the equation: 27W - W² = 180

Rearranging it further: W² - 27W + 180 = 0

Now, we have a quadratic equation in terms of W. We can solve this equation to find the possible values of W.

Using the quadratic formula: W = (-b ± √(b² - 4ac)) / (2a)

For our equation, the values of a, b, and c are: a = 1, b = -27, c = 180

Substituting these values into the quadratic formula, we get: W = (-(-27) ± √((-27)² - 4 × 1 × 180)) / (2 × 1)

Simplifying further: W = (27 ± √(729 - 720)) / 2 W = (27 ± √9) / 2 W = (27 ± 3) / 2

This gives us two possible values for W: 1. When W = (27 + 3) / 2 = 30 / 2 = 15 2. When W = (27 - 3) / 2 = 24 / 2 = 12

Now, let's substitute these values of W back into the equation for the perimeter to find the corresponding values of L.

For W = 15: L + 15 = 27 L = 27 - 15 L = 12

For W = 12: L + 12 = 27 L = 27 - 12 L = 15

Therefore, the sides of the rectangle can be either: - Length = 12 cm, Width = 15 cm - Length = 15 cm, Width = 12 cm

So, the possible sides of the rectangle are 12 cm and 15 cm.

Please let me know if I can help you with anything else.