A rectangle has one side that is 6 cm shorter t... - JAMB Mathematics 2023 Question

Let's denote the length of the longer side of the rectangle as \(L\) and the length of the shorter side as \(L - 6\).

The area of the rectangle is given by \(A = L \times (L - 6)\).

According to the problem, if we add 2 cm to each side, the new dimensions will be \(L + 2\) and \((L - 6) + 2\) (or \(L - 4\)).

The new area will be \((L + 2) \times (L - 4)\).

The problem states that the area increases by 68 cm\(^2\), so we can set up the equation:

\[(L + 2) \times (L - 4) = L \times (L - 6) + 68\]

Now, let's solve for \(L\):

\[L^2 - 4L + 2L - 8 = L^2 - 6L + 68\]

Combine like terms:

\[L^2 - 2L - 8 = L^2 - 6L + 68\]

Subtract \(L^2\) from both sides:

\[-2L - 8 = -6L + 68\]

Add \(6L\) to both sides:

\[4L - 8 = 68\]

Add 8 to both sides:

\[4L = 76\]

Divide by 4:

\[L = 19\]

Now that we have the length of the longer side (\(L = 19\)), we can find the length of the shorter side (\(L - 6\)):

\[L - 6 = 19 - 6 = 13\]

Therefore, the correct answer is 13 cm