Engineering Board Exam Reviewer · Properties of Triangles · hard

The three altitudes of a triangle are 12, 15 and 20 units long. Find the area of the triangle.

  1. 150
  2. 75
  3. 300
  4. 120

Answer

A. 150

Solution

The sides are proportional to 112: 115: 120=5:4:3, a right triangle. The altitudes to the two legs equal the other leg: 3k=15 and 4k=20 give k=5, so the legs are 15 and 20 and the area is 12(15)(20)=150.

More Properties of Triangles questions

  1. In triangle ABC, BC=14, CA=15 and AB=13. Find the distance from vertex A to the incenter.
  2. Find the area of a triangle with sides 9, 10 and 17.
  3. A triangle is inscribed in a circle of radius 10. Find the side opposite an angle of 30°.
  4. For the triangle with sides a=13, b=14 and c=15, find the exradius opposite side a.
  5. Find the radius of the inscribed circle of a right triangle with legs 6 and 8.
  6. In triangle ABC, BC=6, CA=9 and AB=10. The bisector of angle C meets AB at D. Find the length of DB.
  7. Find the altitude to the longest side of the triangle with sides 13, 14 and 15.
  8. In the triangle with sides 13, 14 and 15, find the length of the median drawn to the side of length 14.
  9. Find the radius of the circumscribed circle of the triangle with sides 13, 14 and 15.
  10. Find the radius of the inscribed circle of the triangle with sides 13, 14 and 15.

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