Question

Периметр прямоугольника 36 см. Сумма длин трёх его сторон 25 см. Чему равна площадь этого прямоугольника? Запиши пояснение для каждого действия в приведённом решении и закончи его.

Answer 1

1) 36см - 25 см = 11 см ( длина четвёртой стороны А) ;                         2) 11см + 11см = 22см ( сумма двух длин А+А) ;                                     3) (36см - 22см) : 2 =   14 : 2 = 7см ( длина стороны В прямоугольника );                                                                                   4) Sпр = А*В   = 11 см * 7см = 77см2.                                                        Ответ: площадь пр. = 77см2.                  

Answer 2

Problem Analysis

We are given that the perimeter of a rectangle is 36 cm and the sum of the lengths of three of its sides is 25 cm. We need to find the area of this rectangle.

Solution

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

We know that the perimeter of a rectangle is given by the formula: Perimeter = 2(L + W). Given that the perimeter is 36 cm, we can write the equation as: 2(L + W) = 36.

We are also given that the sum of the lengths of three sides is 25 cm. Since a rectangle has two pairs of equal sides, we can write the equation as: L + W + L = 25.

Now we have a system of equations: 1. 2(L + W) = 36 2. L + W + L = 25

We can solve this system of equations to find the values of L and W.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From equation 2, we can rewrite it as: 2L + W = 25.

Now we can substitute this value of W into equation 1:

2(L + (25 - 2L)) = 36

Simplifying the equation:

2(25 - L) = 36

50 - 2L = 36

-2L = 36 - 50

-2L = -14

Dividing both sides by -2:

L = -14 / -2

L = 7

Now we can substitute the value of L back into equation 2 to find W:

7 + W + 7 = 25

W + 14 = 25

W = 25 - 14

W = 11

So the length of the rectangle is 7 cm and the width is 11 cm.

Calculating the Area

The area of a rectangle is given by the formula: Area = Length x Width.

Substituting the values we found:

Area = 7 cm x 11 cm

Area = 77 cm²

Therefore, the area of the rectangle is 77 cm².

Conclusion

The area of the given rectangle with a perimeter of 36 cm and a sum of the lengths of three sides of 25 cm is 77 cm².