Question

Периметр прямоугольника равен 240см. Если длину прямоугольника уменьшить на 14см, а ширину увеличить на 10см, то его площадь увеличится на 4 см(квадратных). Найдите стороны прямоугольника.РЕШИТЬ ЗАДАЧУ НАДО ИСПОЛЬЗУЯ ТОЛЬКО х, И ЕСЛИ КТО СМОГ РЕШИТЬ НАПИШИТЕ КРАТКУЮ ЗАПИСЬ ПОЖАЛУЙСТА*)) ЗАРАНЕЕ СПАСИБО*)

Answer 1

Р(прямоугольник)=2(a+b)
a+b=P/2
a=P/2-b
b=P/2-a
P=240
a+b=240/2=120
Пусть а=х, тогда
b=240/2-x
b=120-x
S(прямоугольника)=a*b
a*b=x*(120-x)
(a-14)*(b+10)=S+4
(x-14)*(120-x+10)=x*(120-x)+4
(x-14)*(130-x)=120x-x²+4
130x-x²-1820+14x-120x+x²-4=0
24x-1824=0
24x=1824
x=1824/24
x=76
120-x=120-76=44
Ответ:a=x=76 см
           b=120-x=44 см
Проверка:
Р=2(a+b)
240=2(76+44)
240=240
S=a*b
76*44=3344
(76-14)*(44+10)=62*54=3348
3348-33484=4

Answer 2

Problem Analysis

We are given that the perimeter of a rectangle is 240 cm. If we decrease the length of the rectangle by 14 cm and increase the width by 10 cm, the area of the rectangle will increase by 4 square cm. We need to find the sides of the rectangle using only the variable 'x'.

Solution

Let's assume the length of the rectangle is 'x' cm and the width is 'y' cm.

We know that the perimeter of a rectangle is given by the formula: perimeter = 2(length + width).

According to the problem, the perimeter of the rectangle is 240 cm. So we can write the equation as:

2(x + y) = 240 Simplifying the equation, we get:

x + y = 120 We are also given that if we decrease the length of the rectangle by 14 cm and increase the width by 10 cm, the area of the rectangle will increase by 4 square cm. The formula for the area of a rectangle is: area = length * width.

So, the original area of the rectangle is: x * y.

After decreasing the length by 14 cm and increasing the width by 10 cm, the new area of the rectangle is: (x - 14) * (y + 10).

According to the problem, the new area is 4 square cm more than the original area. So we can write the equation as:

(x - 14) * (y + 10) = x * y + 4 Expanding and simplifying the equation, we get:

xy - 14y + 10x - 140 = xy + 4 Simplifying further, we get:

10x - 14y = 144 Now we have a system of two equations with two variables:

Equation 1: x + y = 120 Equation 2: 10x - 14y = 144 We can solve this system of equations to find the values of 'x' and 'y'.

Let's solve the system of equations:

From Equation 1, we can express 'x' in terms of 'y':

x = 120 - y

Substituting this value of 'x' into Equation 2, we get:

10(120 - y) - 14y = 144

Simplifying the equation, we get:

1200 - 10y - 14y = 144

Combining like terms, we get:

-24y = -1056

Dividing both sides by -24, we get:

y = 44

Substituting this value of 'y' back into Equation 1, we get:

x + 44 = 120

Simplifying the equation, we get:

x = 76

Therefore, the sides of the rectangle are 76 cm and 44 cm.

Answer

The sides of the rectangle are 76 cm and 44 cm.