# CAT Practice : Coordinate Geometry

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In an acute triangle, the sum of the squares of the two smaller sides must be larger than the square of the third side

## Isosceles Triangle

Q.23: An acute-angled isosceles triangle has two of its sides equal to 10 and 16. Find the area of this triangle.
1. $\sqrt{231}$ units
2. 12 $\sqrt{66}$ units
3. 24 units
4. 5 $\sqrt{231}$ units

Choice (D).5 $\sqrt{231}$ units

## Detailed Solution

The given triangle is an acute angled isosceles triangle.
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 = $\frac{(10 + 16 + 16)}{2}$ = 21

Area = $\sqrt{21 (21 - 16) (21 - 16) (21 - 10)}$

= $\sqrt{21 * 5 * 5 * 11}$

= 5 $\sqrt{231}$units

Correct Answer: 5 $\sqrt{231}$ units

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