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. 107
    2. 87
    3. 7.57
    4. 157

 

  • Correct Answer
    Choice (C). 7.57

Explanatory Answer

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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 ADB and ADC are congruent.

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

DC = 15

AD2 + DC2 = AC2

AD2 + 152 = 202

AD2 = 400 – 225

AD2 = 175

AD = 57

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 57 = 1/2 x (20 x h)

h = 3/2 x 57

= 7.57

Answer choice (c).

Correct Answer: 7.57



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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.