Question

if the perimeter of a square is 20 cm.

find the area and length of diagonal

Answer 1

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Answer 2

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Here is the solution:

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Perimeter of a square = 20 cm

Find the length:

Perimeter = 4 x Length

20 = 4 x Length

Length = 20 ÷ 4 = 5 cm

Find the length of the diagonals:

a² + b² = c²

c² = 5² + 5²

c² = 50

c = √50

c = 5√2 cm

Find the area:

Area = Length x Length

Area = 5 x 5  = 25 cm²

Answer: Length = 2√50 and the area = 25 cm²

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ALTERNATIVE METHOD TO FIND THE LENGTH OF THE DIAGONAL OF A SQUARE:

Length of the diagonal of a square = side√2

we found the length of the square is 5 cm,

therefore the length of the diagonal is 5√2

Answer: The length of the diagonal is 5√2