Find the area and perimeter of a square whose length of diagonals is 20\(\sqrt2\) cm....
MATHEMATICS
JAMB 2023
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
Correct Answer: D. 400 cm\(^2\), 80 cm
Explanation
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
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