Find the area and perimeter of a square whose length of diagonals is 20\(\sqrt2\) cm.
A
800 cm\(^2\), 80 cm
B
400 cm, 80 cm\(^2\)
C
80 cm, 800 cm\(^2\)
D
400 cm\(^2\), 80 cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Using Pythagoras theorem
⇒ \((20\sqrt2)2 = x^2 + x^2\)
⇒ 800 = \(2x^2\)
⇒ 400 = \(x^2\)
⇒ x = \(\sqrt400\) = 20 cm
∴ Area of a square = \(x^2 = 20^2 = 400 cm^2\)
∴ Perimeter of a square = 4x = 4 x 20 = 80 cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #67380)