Question

Длинну прямоугольника уменьшили на 4 см и получили квадрат площадь котораго меньше площади прямоугольника на 12см(2) Найдите сторону квадрата...

Answer 1

A - длина прямоугольника
b - ширина
Тогда:
               (a - 4)b + 12 = ab
                ab - 4b + 12 = ab
                4b = 12
                 b = 3 (см) - ширина, она же - сторона квадрата.

Ответ: 3 см  

Answer 2

Problem Analysis

We are given that the length of a rectangle is reduced by 4 cm, resulting in a square with an area 12 cm² less than the area of the rectangle. We need to find the side length of the square.

Solution

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

According to the problem, the length of the rectangle is reduced by 4 cm, so the new length is L - 4 cm.

We are also given that the resulting square has an area 12 cm² less than the area of the rectangle. The area of the rectangle is L * W cm², and the area of the square is (L - 4) * (L - 4) cm².

We can set up the equation: (L - 4) * (L - 4) = L * W - 12

To solve this equation, we can expand the left side and simplify: L² - 8L + 16 = L * W - 12

Rearranging the equation, we get: L² - W * L + 16 - 12 = 0 L² - W * L + 4 = 0

Now, we can use the quadratic formula to solve for L: L = (-(-W) ± √((-W)² - 4 * 1 * 4)) / (2 * 1) L = (W ± √(W² - 16)) / 2

Since we are looking for a positive length, we can ignore the negative solution. Therefore, we have: L = (W + √(W² - 16)) / 2

Now, let's substitute this value of L into the equation for the area of the square: (L - 4) * (L - 4) = L * W - 12

Expanding and simplifying: L² - 8L + 16 = L * W - 12

Substituting the value of L: ((W + √(W² - 16)) / 2)² - 8((W + √(W² - 16)) / 2) + 16 = (W + √(W² - 16)) * W - 12

Simplifying further: ((W + √(W² - 16))² - 16(W + √(W² - 16)) + 32 = W² + √(W² - 16) * W - 12

Expanding and simplifying: W² + 2W√(W² - 16) + (W² - 16) - 16W - 16√(W² - 16) + 32 = W² + √(W² - 16) * W - 12

Canceling out the common terms: 2W√(W² - 16) - 16W - 16√(W² - 16) + 16 = √(W² - 16) * W - 44

Rearranging the equation: 2W√(W² - 16) - √(W² - 16) * W - 16W + 16√(W² - 16) = -44 - 16

Simplifying further: W(2√(W² - 16) - √(W² - 16)) - 16W + 16√(W² - 16) = -60

Factoring out √(W² - 16): √(W² - 16)(2W - W) - 16W + 16√(W² - 16) = -60

Simplifying: √(W² - 16)(W - 16) = -60

Since the square root of a number is always positive, we can ignore the negative solution. Therefore, we have: √(W² - 16) = -60 / (W - 16)

Squaring both sides of the equation: W² - 16 = (60 / (W - 16))²

Expanding and simplifying: W² - 16 = 3600 / (W - 16)²

Cross-multiplying: W²(W - 16)² - 16(W - 16)² = 3600

Expanding and simplifying: W⁴ - 32W³ + 256W² - 16W³ + 512W - 4096 - 3600 = 0

Combining like terms: W⁴ - 48W³ + 256W² + 512W - 7696 = 0

Now, we can solve this quartic equation to find the value of W. However, solving quartic equations can be complex and time-consuming. Since the problem does not specify the exact value of W, we can use numerical methods or approximation techniques to find an approximate value for W.

Please note that the solution provided above is based on the information provided in the problem statement. If there are any additional constraints or information, please let me know, and I'll be happy to assist you further.