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Equal Angles Subtend Equal Sides

Given : In ...

Question

Given : In $Δ A B C, A C = 4 x, B C = 6 x - 6, A B = 5 x - 8 a n d ∠ A = ∠ B$ . Find the perimeter of $Δ A B C$ .

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Solution

Given, $∠ A = ∠ B$
Hence, $A C = B C$ (Isosceles triangle property)
$4 x = 6 x - 6$
$- 2 x = - 6$
$x = 3$
thus, $A B = 7$ cm, $B C = 12$ cm, $A C = 12$ cm
Perimeter = $A B + B C + A C$
= $7 + 12 + 12$
= $31$ cm

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