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The question is from CAT Geometry - Triangles. It tests our understanding on properties of a triangle. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. In this question it discusses about the properties of altitude of a triangle.

Question 12: Find the altitude to side AC of triangle with side AB = 20 cm, AC = 20 cm, BC = 30 cm.

  1. 10√7
  2. 8√7
  3. 7.5√7
  4. 15√7

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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. Geometry - triangles: CAT Geometry Altitude of a Triangle
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."

Hence, the answer is 7.5√7.

Choice C is the correct answer.


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