Question

.Площа прямокутника дорівнює 48 см. Знайдіть його сторони, якщо їх півсума дорівнює 7 см.​

Answer 1

Ответ:

6 і 8 см

Объяснение:

ху=48

х+у=14

х=14-у

(14-у)у=48

у²-14у+48=0

6;8

Answer 2

Finding the Sides of a Rectangle

To find the sides of a rectangle when the area and half the sum of its sides are given, we can use the following steps:

1. Identify the Given Values: - Area of the rectangle = 48 sq cm - Half the sum of its sides = 7 cm

2. Formulate the Equations: Let's assume the sides of the rectangle are represented by 'a' and 'b'. We know that the area of a rectangle is given by the formula: Area = length * width. So, we have the equation: \[a \times b = 48\] We are also given that the half sum of the sides is 7 cm, which gives us the equation: \[\frac{a + b}{2} = 7\]

3. Solve the Equations: We can use the second equation to express one of the variables in terms of the other and then substitute it into the first equation to solve for the sides of the rectangle.

Let's proceed with solving the equations to find the sides of the rectangle.

Solution

Using the given information, we can solve for the sides of the rectangle as follows:

From the equation \(\frac{a + b}{2} = 7\), we can express one of the variables in terms of the other: \[a + b = 14\] \[a = 14 - b\]

Substitute \(a = 14 - b\) into the equation \(a \times b = 48\): \[(14 - b) \times b = 48\] \[14b - b^2 = 48\] \[b^2 - 14b + 48 = 0\]

Using the quadratic formula, we can solve for 'b': \[b = \frac{-(-14) \pm \sqrt{(-14)^2 - 4 \times 1 \times 48}}{2 \times 1}\] \[b = \frac{14 \pm \sqrt{196 - 192}}{2}\] \[b = \frac{14 \pm \sqrt{4}}{2}\] \[b = \frac{14 \pm 2}{2}\]

So, we have two possible values for 'b': \[b_1 = \frac{14 + 2}{2} = 8\] \[b_2 = \frac{14 - 2}{2} = 6\]

Now that we have the values of 'b', we can find the corresponding values of 'a': \[a_1 = 14 - 8 = 6\] \[a_2 = 14 - 6 = 8\]

Conclusion

Therefore, the sides of the rectangle can be either: - 6 cm and 8 cm - 8 cm and 6 cm

These are the possible combinations of sides for a rectangle with an area of 48 sq cm and half the sum of its sides equal to 7 cm.