1 hình chữ nhật có chu vi bằng 132m .Nếu tăng chiều dài thêm 8m và giảm chiều rộng đi 4m thì diện tích hình chữ tăng thêm 52m$^{2{}}$.Tính các kích thước của hình chữ nhật

To solve this problem, we can use the information given to set up a system of equations. Let's denote the length of the rectangle as \( l \) and the width as \( w \). We are given that the perimeter of the rectangle is 132m, so we have the equation: \[ 2l + 2w = 132 \] We are also given that if we increase the length by 8m and decrease the width by 4m, then the area increases by 52m\(^2\). This gives us another equation: \[ (l+8)(w-4) - lw = 52 \] Now, let's solve this system of equations to find the values of \( l \) and \( w \). First, let's simplify the second equation: \[ lw + 8w - 4l -32 - lw = 52 \] \[ 8w - 4l -32 = 52 \] \[ 8w - 4l = 84 \] \[ 2w - l =21 \] Now we have a system of equations: \[ \begin{cases} 2l + 2w =132 \\ 2w - l =21 \end{cases} \] Solving this system of equations will give us the values for \( l \) and \( w \). We can use substitution or elimination method to solve it. Using substitution method: From equation (2), we get: \[ l=2w-21 \] Substitute this into equation (1): \[2(2w-21)+2w=132\] \[4w-42+2w=132\] \[6w=174\] \[w=29\] Then substitute back to find \( l \): \[l=2*29-21=37\] So, the dimensions of the rectangle are: Length: \(37\) m Width: \(29\) m