CAT Practice : Geometry-Triangles

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Alitude of a Triangle

Alitude of a Triangle

Q.12: Find the altitude to side AC of triangle with side AB = 20 cm, AC = 20 cm, BC = 30 cm.
1. 10${\surd }$7
2. 8${\surd }$7
3. 7.5${\surd }$7
4. 15${\surd }$7

Choice (C). 7.5${\surd }$7

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Detailed Solution

This is an isosceles triangle. So, let us find the altitude to BC first.

Altitude to BC bisects BC as ${\triangle }$ADB and ${\triangle }$ADC are congruent.

{RHS congruence; AD is common, AB = AC}

DC = 15

AD = 5${\surd }$7

Area of the triangle = 1/2 x base x height

= 1/2 x BC x AD or 1/2 x AC x (altitude to AC, say, h)

= 1/2 x 30 x 5${\surd }$7 = 1/2 x (20 x h)

h = 3/2 x 5${\surd }$7

= 7.5${\surd }$7

Correct Answer: 7.5${\surd }$7

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.