Find the area and perimeter of a square whose l... - JAMB Mathematics 2023 Question

Let's denote the length of the side of the square as \(s\) and the length of the diagonal as \(d\). For a square, the length of the diagonal is related to the side length by \(d = s\sqrt{2}\).

Given that \(d = 20\sqrt{2}\), we can equate this to the diagonal formula:

\[s\sqrt{2} = 20\sqrt{2}\]

Now, solving for \(s\):

\[s = \frac{20\sqrt{2}}{\sqrt{2}}\]

\[s = 20\]

Now, we can find the area (\(A\)) and perimeter (\(P\)) of the square:

Area of a square: \(A = s^2\)

Perimeter of a square: \(P = 4s\)

Substitute the value of \(s\) into these formulas:

\[A = 20^2 = 400 \, \text{cm}^2\]

\[P = 4 \times 20 = 80 \, \text{cm}\]