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Question
Find the perimeter of a square if its diagonal is `10sqrt2` cm:
Options
10 cm
`40sqrt2` cm
20 cm
40 cm
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Solution
40 cm
Explanation:
It is given that ABCD is a square.
∴ AB = BC = CD = DA = x (say)
According to Pythagoras theorem, in ∆ABD
AB2 + AD2 = BD2
⇒ `x^2 + x^2 = (10sqrt2)^2`
⇒ 2x2 = 200
⇒ x2 = 100
⇒ x = `sqrt100`
x = 10 cm
Hence, the side of the square is 10 cm.
Now, Perimeter of a square = 4 × side
= 4 × x
= 4 × 10
= 40
Hence, the correct option is 40 cm.
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