Question

Площадь прямоугольника 24квадрадных см,а периметр20см.начети этот прямоугольник.

Answer 1

Стороны прямоугольника равны 4 и 6 см.

6*4=24 квадратных см - площадь

4+6+4+6=20 см - периметр 

Answer 2

P=(a+b)*2

a+b=P:2

a+b=20:2=10 (cм) - сумма длины и ширины прямоугольника

S=a*b

a*b=24 кв.см

Подберём такие a и b, чтобы a+b=10 см, a a*b=24 кв.см

 

a=6 см, b=4 cм или a=4 см, b=6 см

 

Следует начертить прямоугольник со сторонами 6 см и 4 см.

Answer 3

Calculation of the Rectangle's Dimensions

To find the dimensions of the rectangle with a given area of 24 square centimeters and a perimeter of 20 centimeters, we can use the formulas for the perimeter and area of a rectangle.

Let's assume the length of the rectangle is a and the width is b.

The perimeter of a rectangle is given by the formula: P = 2(a + b).

The area of a rectangle is given by the formula: A = a * b.

We are given that the perimeter is 20 centimeters, so we can write the equation: 20 = 2(a + b).

We are also given that the area is 24 square centimeters, so we can write the equation: 24 = a * b.

Now we have a system of two equations with two variables. We can solve this system to find the dimensions of the rectangle.

Solving the System of Equations

Let's solve the system of equations using substitution.

From the equation 20 = 2(a + b), we can isolate a in terms of b: a = (20 - 2b) / 2.

Substituting this value of a into the equation 24 = a * b, we get: (20 - 2b) / 2 * b = 24.

Simplifying the equation, we have: 20b - 2b^2 = 48.

Rearranging the equation, we get a quadratic equation: 2b^2 - 20b + 48 = 0.

We can solve this quadratic equation to find the values of b.

Solving the Quadratic Equation

Using the quadratic formula, b = (-b ± √(b^2 - 4ac)) / (2a), where a = 2, b = -20, and c = 48, we can calculate the values of b.

Substituting the values into the quadratic formula, we have: b = (-(-20) ± √((-20)^2 - 4 * 2 * 48)) / (2 * 2).

Simplifying the equation, we get: b = (20 ± √(400 - 384)) / 4.

Further simplification gives us: b = (20 ± √16) / 4.

Taking the square root of 16, we have: b = (20 ± 4) / 4.

This gives us two possible values for b: 1. b = (20 + 4) / 4 = 6 2. b = (20 - 4) / 4 = 4

Now that we have the values of b, we can substitute them back into the equation a = (20 - 2b) / 2 to find the corresponding values of a.

For b = 6, we have: a = (20 - 2 * 6) / 2 = 4.

For b = 4, we have: a = (20 - 2 * 4) / 2 = 6.

Therefore, the dimensions of the rectangle are: 1. Length (a) = 4 centimeters, Width (b) = 6 centimeters. 2. Length (a) = 6 centimeters, Width (b) = 4 centimeters.

Conclusion

The rectangle can have two possible sets of dimensions: 4 centimeters by 6 centimeters or 6 centimeters by 4 centimeters.