Question

На листе нарисованы три прямоугольника А, Б и В (см. рисунок). У прямоугольников А и Б одинаковая ширина, а у прямоугольников Б и В — одинаковая длина (ширина — сверху вниз, длина — слева направо). Длина прямоугольника Б больше длины прямоугольника А на 4 см, и площадь Б больше площади А на 28 см2. Ширина прямоугольника В больше ширины прямоугольника Б на 3 см, и площадь В больше площади Б на 39 см2. Найдите площадь прямоугольника А в квадратных сантиметрах.

Answer 1

Ответ:

Пошаговое объяснение:

SA=30м².

SB=56²

SБ=40м²

Answer 2

Problem Analysis

We are given three rectangles labeled A, B, and C. Rectangles A and B have the same width, while rectangles B and C have the same length. The length of rectangle B is 4 cm greater than the length of rectangle A, and the area of rectangle B is 28 cm² greater than the area of rectangle A. The width of rectangle C is 3 cm greater than the width of rectangle B, and the area of rectangle C is 39 cm² greater than the area of rectangle B. We need to find the area of rectangle A in square centimeters.

Solution

Let's denote the width of rectangle A as w, the length of rectangle A as l, and the area of rectangle A as A.

Given that the length of rectangle B is 4 cm greater than the length of rectangle A, we can express the length of rectangle B as l + 4.

We are also told that the area of rectangle B is 28 cm² greater than the area of rectangle A. Therefore, we can write the equation: (w)(l + 4) = A + 28.

Similarly, the width of rectangle C is 3 cm greater than the width of rectangle B, so we can express the width of rectangle C as w + 3.

The area of rectangle C is 39 cm² greater than the area of rectangle B. Therefore, we can write the equation: (w + 3)(l + 4) = A + 28 + 39.

To find the area of rectangle A, we need to solve these equations.

Solving the Equations

Let's simplify the equations and solve them step by step.

Equation 1: (w)(l + 4) = A + 28

Equation 2: (w + 3)(l + 4) = A + 28 + 39

Expanding Equation 2:

wl + 4w + 3l + 12 = A + 67

Now, we have two equations:

Equation 1: wl + 4w = A + 28

Equation 2: wl + 4w + 3l = A + 67

Subtracting Equation 1 from Equation 2:

(wl + 4w + 3l) - (wl + 4w) = (A + 67) - (A + 28)

Simplifying:

3l = 39

Dividing both sides by 3:

l = 13

Now, we can substitute the value of l into Equation 1 to find the value of w:

w(13 + 4) = A + 28

w(17) = A + 28

Dividing both sides by 17:

w = (A + 28) / 17

Now, we have the values of l and w. We can substitute them into Equation 1 to find the value of A:

(A + 28) / 17 * (13 + 4) = A + 28

Simplifying:

A + 28 = (A + 28) / 17 * 17

A + 28 = A + 28

This equation is true for any value of A. Therefore, the value of A can be any real number.

Answer

The area of rectangle A can be any real number in square centimeters.