The perimeter of an isosceles triangle is 64 cm and each of the equal sides is 5 6 times the base Wh...........

Quantitative Aptitude (CPO) Mensuration 2D

The perimeter of an isosceles triangle is 64 cm and each of the equal sides is 5/6 times the base. What is the area (in cm2) of the triangle?

Options:

169

192

196

184

- In an isosceles triangle, two sides are equal, and the perimeter is given as 64 cm.

- Let the base of the triangle be 'b' cm.

- Then each of the equal sides = (5/6) * b cm.

- The perimeter equation is: b + 2*(5/6)*b = 64.

- Simplifying, we get b/3 + 10b/6 = 64, leading to 16b/6 = 64.

- Solving for b gives b = 24 cm.

- Each equal side = (5/6)*24 = 20 cm.

- Now, to find the area, use Heron's formula.

- Semi-perimeter, s = (24 + 20 + 20) / 2 = 32 cm.

- Area = v[s(s-24)(s-20)(s-20)].

- Calculating, Area = v[32*(32-24)*(32-20)*(32-20)] = v[32*8*12*12] = v36864 = 192 cm².

- Therefore, Option 2: 192 is correct.

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