First slide

Properties of triangles

Question

${The sides of a triangle ABC satisfy the relations a+b-c=2 and 2ab-c}^{2} = 4 . t hen square of the area of triangle is$

Moderate

A

1
B

2
C

3
D

4

Solution

$a + b - c = 2 - - - - (1)$
${and 2ab-c}^{2} =4----- (2)$
$\Rightarrow a^{2} + b^{2} + c^{2} + 2 a b - 2 b c - 2 c a = 4 = 2 a b - c^{2}$
$\Rightarrow {(b - c)}^{2} + {(a - c)}^{2} = 0$
$\Rightarrow a = b = c$
triangle is equilateral
$\Rightarrow a = 2$
$\Rightarrow ∆ = \sqrt{3}$

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