CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

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

Video Explanation

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."