The perimeter of an isosceles triangle is 544 cm and each

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The perimeter of an isosceles triangle is 544 cm and each of the equal sides is 5/6 times the base. What is the area (in cm²) of the triangle ?

Let AD be the altitude.
Base = x cm

Each equal side =	5x	cm
	6

∴ x + 2 ×	5x	= 544
	6

⇒	3x + 5x	= 544
	3

⇒ 8x = 544 × 3

⇒ x =	544 × 3	= 204
	8

∴ BD = 102 cm

⇒ AB =	5x	=	5 × 204	= 170 cm
	6		6

and AD = √AB² - BD²
= √170² - 102²
= √(170 + 102)(170 - 102)
= √272 × 68 = 136cm

∴ ∆ ABC =	1	BC × AD
	2

=	1	× 204 × 136
	2

= 13872 sq.cm.