Find an area of an isosceles triangle, which has perimeter of 32 cm and the altitude of 8 cm.
Option:
A. 24 Sq. cm
B. 40 Sq. cm
C. 48 Sq. cm
D. 60 Sq. cm
Answer: C . 48 Sq. cm
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Justification:
An isosceles triangle has two equal sides = X.
Perimeter P = 32 = X + X + Base (B)
=> B = 32 - 2X => B/2 = 16 - X
Now the X = Sq. root of ( 8^2 + B^2) = Sq. root of (8^2 + (16-X)^2)
=> X^2 = 8^2 + (16-X)^2 => X = 10
=> B = 12
The area of the isosceles triangle A = (1/2) * Altitude * Base = (1/2) * 8 * 12 = 48 Sq. cm
