CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

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Explanatory Answer

Method of solving this CAT Question from Triangles: Understanding the basic properties of altitude of a triangle will help to solve.

This is an isosceles triangle. So, let us find the altitude to BC first.
Altitude to BC bisects BC as △ADB and △ADC are congruent.
{RHS congruence; AD is common, AB = AC}
DC = 15
AD² + DC ² = AC²
AD² + 15 ² = 20²
AD² = 400 - 225
AD² = 175
AD = 5√7
Area of the triangle = \\frac{1}{2}\\) * base * height
= \\frac{1}{2}\\) * BC * AD or \\frac{1}{2}\\) * AC * (altitude to AC, say, h)
= \\frac{1}{2}\\) * 30 * 5√7 = \\frac{1}{2}\\) * (20 * h)
h = \\frac{3}{2}\\) * 5√7
h = 7.5√7

The question is " Find the altitude to side AC of triangle with side AB = 20 cm, AC = 20 cm, BC = 30 cm."