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JAMB Mathematics 2023 Paper

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Question : 57

Total: 80

Find the area and perimeter of a square whose length of diagonals is 20

\sqrt{2}

cm.

800 cm ${}^2$ , 80 cm
400 cm, 80 cm ${}^2$
80 cm, 800 cm ${}^2$
400 cm ${}^2$ , 80 cm

Solution:

Concept:

For a square, diagonal

= x\sqrt{2}

, area

= x^2

, and perimeter

= 4x

.

Explanation:

Let the side of the square be

x

cm.

Given diagonal

= 20\sqrt{2}

cm.

Using Pythagoras theorem:

(20\sqrt{2})^2 = x^2 + x^2

.

So,

800 = 2x^2

.

Divide both sides by 2:

400 = x^2

.

Thus,

x = 20

cm.

Area of square

= x^2 = 20^2 = 400

cm

^2

.

Perimeter of square

= 4x = 4 \times 20 = 80

cm.

Answer:

D.

400

cm

^2

,

80

cm.

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