# CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

###### CAT Questions | CAT Geometry Questions | Isosceles Triangles

The question is from CAT Geometry - Triangles. In this problem two sides of a triangle are given and we have to find the area of the triangle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. Here, we have to find out the third side and then proceed to the area of the triangle.

Question 23: An acute-angled isosceles triangle has two of its sides equal to 10 and 16. Find the area of this triangle.

1. √231 units
2. 12√66 units
3. 24 units
4. 5√231 units

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##### Method of solving this CAT Question from Triangles: In an acute triangle, the sum of the squares of the two smaller sides must be larger than the square of the third side.

The third side is either 10 or 16 and the sum of the squares of the two smaller sides must be greater than the square of the third side.
102 + 102 < 162
Therefore, the third side of the triangle is 16.
Semiperimeter, S = (10 + 16 + 16)/2 = 21
Area = √(21(21−16)(21−16)(21−10))
= √(21 * 5 * 5 * 11)
= 5√231 units

The question is "Find the area of this triangle."

##### Hence, the answer is 5√231 units.

Choice D is the correct answer.

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