# Each of the equal

Let height of triangle = h cm

Given: Base of the triangle (b) = 12 cm

Equal sides (a) = h + 2 cm

Now,

Area of a triangle = 1/2 × Base × Height

And,

Area of isosceles triangle = 1/4 × b√(4a2 – b2)

1/2 × Base × Height = 1/4 × b√(4a2 – b2)

1/2 × 12 × h = 1/4 × 12√[4(h + 2)2 – 122]

6h = 3√(4h2 + 16h + 16-144)

2h = √(4h2 + 16h-128)

On squaring both sides we get,

4h2 = 4h2 + 16h – 128

16h – 128 = 0

16h = 128

h = 8 cm

Now,

Area of a triangle = 1/2 × Base × Height

= 1/2 × 12 cm × 8 cm

= 1/2 × 96 cm2

= 48 cm2

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