Answer:
Let's denote the length of the rectangle as \(L\) and the width as \(W\).
According to the problem:
1. The area of the rectangle is 150 cm², so we have the equation:
\[L \cdot W = 150\]
2. The width of the rectangle is 5 cm shorter than the length, which can be written as:
\[W = L - 5\]
We can use these two equations to solve for the values of \(L\) and \(W\).
Substitute the second equation into the first:
\[L \cdot (L - 5) = 150\]
Expand and rearrange:
\[L^2 - 5L - 150 = 0\]
This is a quadratic equation. Factor it or use the quadratic formula to find the solutions for \(L\). Once you have \(L\), you can find \(W\) using the second equation.
Once you have the values of \(L\) and \(W\), remember that the sides of the square are the same length as the width of the rectangle, which is \(W\). So, the area of the square will be \(W^2\).
Explanation: