Mathematics
A square has the perimeter 56 m. Find its area and the length of one diagonal correct up to two decimal places.
Mensuration
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Answer
Let ABCD be a square with side x metres.
Perimeter of square = 4 × side
Substituting the values we get,
⇒ 56 = 4x
⇒ x = = 14 m.
Since, each angle = 90° in a square.
In right angle triangle ABC
Using Pythagoras theorem,
⇒ AC2 = AB2 + BC2
⇒ AC2 = 142 + 142
⇒ AC2 = 196 + 196 = 392
⇒ AC =
⇒ AC = = 14 × 1.414 = 19.80 m.
Area of square = (side)2
= 142 = 196 m2.
Hence, the area of square = 196 m2 and length of diagonal = 19.80 m.
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