Question : 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:
Option 1: 240
Option 2: 180
Option 3: 360
Option 4: 120
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Correct Answer: 120
Solution :
Let the base of the isosceles triangle as
The altitude drawn to the base =
The perimeter of the isosceles triangle =
In an isosceles triangle, the altitude bisects the base, dividing it into two equal parts.
Let each part as
We can use the Pythagorean theorem,
Given that the perimeter of the triangle is
From equation (i) and equation (ii),
From equation (ii),
The area of the triangle
Hence, the correct answer is 120.
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