Question

the two rectangles shown below have equal areas. find the area of both rectangles.
which equation represents the situation?
\\( \frac { 1 } { 2 } + ( s - 4 ) = \frac { 1 } { 2 } + ( s - 3 ) \\)
\\( \frac { 1 } { 2 } + ( s - 3 ) = \frac { 1 } { 4 } + ( s - 4 ) \\)
\\( \frac { 1 } { 2 } ( s - 3 ) = \frac { 1 } { 4 } ( s - 4 ) \\)
\\( \frac { 1 } { 2 } ( s - 4 ) = \frac { 1 } { 4 } ( s - 3 ) \\)

Explanation:

Step 1: Formula for the area of a rectangle

The area of a rectangle is given by \(A = \text{length}\times\text{width}\).
For the first rectangle with width \(\frac{1}{2}\) and length \(s - 4\), its area \(A_1=\frac{1}{2}(s - 4)\).
For the second rectangle with width \(\frac{1}{4}\) and length \(s - 3\), its area \(A_2=\frac{1}{4}(s - 3)\).

Step 2: Set up the equation

Since the two rectangles have equal areas (\(A_1 = A_2\)), we get the equation \(\frac{1}{2}(s - 4)=\frac{1}{4}(s - 3)\).

Answer:

\(\frac{1}{2}(s - 4)=\frac{1}{4}(s - 3)\) (the fourth option in the given list of equations)