The altitude drawn to the base of an isosceles triangle

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The altitude drawn to the base of an isosceles triangle is 8 cm and its perimeter is 64 cm. The area (in cm²) of the triangle is

Let AB = AC = x cm
and BD = DC = y cm
then, AD² = x² – y²
⇒ x² – y² = 64
x + x + 2y = 64
⇒ 2x + 2y = 64
⇒ x + y = 32

∴	x² - y²	=	64
	x + y		32

⇒ x = 17 cm
Also, x + y = 32
⇒ y = 32 – 17 = 15 cm

∴ area of ∆ ABC =	1	× BC × AD
	2

=	1	× 30 × 8 = 120 sq. cm.
	2