Question

Длина прямоугольного листа железа на 4 см больше ширины от этого прямоугольника отрезали две полосы так что остался прямоугольник длина которого на 3 см меньше длины листа если известно что его площадь на 102 кубичиских см больше площади оставшейся части .

Answer 1

х см - ширина листа

х+4 - длина листа

х(х+4)  -площадь листа

После того как отрезали две полоски, получим:

х+4 - 3 = х+1(см) длина оставшейся части

х - 2(см) - ширина оставшейся части

(х+1)(х-2)кв.см - площадь оставшейсячасти.

Составим уравнение

х(х+4) - (х-2)(х+1) = 102

Х2 + 4х –х2 – х +2х +2 = 102 (х в квадрате + 4х минус х в квадрате...)

5х = 100

Х = 20 (см) ширина листа

20+4= 24)см) длина листа

 

Answer 2

Problem Analysis

We are given a rectangular sheet of iron, and two strips have been cut from it. The remaining rectangle is 3 cm shorter in length than the original sheet. We are also told that the area of the remaining rectangle is 102 cubic cm greater than the area of the cut strips.

Let's assume the width of the original sheet is x cm. According to the problem, the length of the sheet is 4 cm longer than its width, so the length is x + 4 cm.

We can set up the following equations based on the given information: 1. The area of the remaining rectangle is 102 cubic cm greater than the area of the cut strips: - Area of the remaining rectangle = Area of the original rectangle - Area of the cut strips - (x + 4 - 3) * x - x * 4 = 102 2. The length of the remaining rectangle is 3 cm shorter than the length of the original sheet: - Length of the remaining rectangle = Length of the original sheet - 3 - x + 4 - 3 = x - 3

We can solve these equations to find the width and length of the original sheet.

Solution

Let's solve the equations to find the width and length of the original sheet.

From equation 2, we have: x + 4 - 3 = x - 3

Simplifying, we get: x + 1 = x - 3

Subtracting x from both sides, we get: 1 = -3

This equation is not possible, which means there is no solution that satisfies the given conditions. It seems there might be an error in the problem statement or the information provided.

Please double-check the problem statement or provide any additional information if available, so we can assist you further.