Question

От листа прямоугольной формы площадь которого равна 840 см сначала отрезали горизонтальную полоску шириной 4 см а затем вертикальную полоску шириной 6 см в результате получился лист квадратной формы найти первоначальные размеры листа

Answer 1

850 сантиметров первоначальный размер листа

Answer 2

Finding the Initial Dimensions of the Rectangular Sheet

To find the initial dimensions of the rectangular sheet, we need to consider the information provided:

- The area of the rectangular sheet is 840 cm². - A horizontal strip with a width of 4 cm was cut from the sheet. - A vertical strip with a width of 6 cm was cut from the sheet. - The resulting shape is a square.

Let's denote the length of the rectangular sheet as L and the width as W.

To find the initial dimensions, we can use the following equation:

L x W = 840 cm² After cutting the horizontal strip, the new length becomes L - 4.

After cutting the vertical strip, the new width becomes W - 6.

Since the resulting shape is a square, the new length and width are equal:

L - 4 = W - 6

Simplifying the equation, we have:

L - W = 2 Now we have a system of equations:

1. L x W = 840 2. L - W = 2

We can solve this system of equations to find the initial dimensions of the rectangular sheet.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination. Let's use the substitution method.

From equation 2, we can express L in terms of W:

L = W + 2

Substituting this value of L into equation 1, we get:

(W + 2) x W = 840

Expanding the equation:

W² + 2W = 840

Rearranging the equation:

W² + 2W - 840 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use factoring.

Factoring the quadratic equation, we get:

(W - 20)(W + 42) = 0

Setting each factor equal to zero, we have:

W - 20 = 0 or W + 42 = 0

Solving for W, we get two possible values:

W = 20 or W = -42

Since the width cannot be negative, we discard the solution W = -42.

Therefore, the width of the rectangular sheet is W = 20 cm.

Substituting this value back into equation 2, we can find the length:

L - 20 = 2

L = 22

Therefore, the length of the rectangular sheet is L = 22 cm.

So, the initial dimensions of the rectangular sheet were 22 cm by 20 cm.

Conclusion

The initial dimensions of the rectangular sheet, before the horizontal and vertical strips were cut, were 22 cm by 20 cm.