The perimeter of a triangle formed by the points (0,0), (1,0)and (0, 1) is …………….units.
The perimeter of a triangle formed by the points (0,0), (1,0)and (0, 1) is …………….units.
A) √2
B) 2 + √2
C) 2 – √2
D) 2 √2
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Correct option is (B) 2 + √2
Given vertices of triangle are \(A(0,0),B(1,0)\;and\;C(0,1).\)
\(\therefore\) \(AB=\sqrt{(1-0)^2+(0-0)^2}\)
\(=\sqrt{1+0}\)
= 1 units,
\(BC=\sqrt{(0-1)^2+(1-0)^2}\)
\(=\sqrt{1+1}\)
= \(\sqrt2\) units
and \(AC=\sqrt{(0-0)^2+(1-0)^2}\)
\(=\sqrt{0+1}\)
= 1 units
\(\therefore\) Perimeter of formed triangle ABC \(=AB+BC+AC\)
\(=(1+\sqrt2+1)\) units
\(=2+\sqrt2\) units
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