Basic Geometric Concepts - Problems on Triangles

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Q1. What is the length of the altitude from the vertex of a triangle with a base of 12 cm and an area of 36 cm²?

Solution:

The area of a triangle is given by Area = 1/2 * base * height. Rearranging gives height = 2 * Area / base = 2 * 36 / 12 = 6 cm.

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Q2. If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, what type of triangle is it?

Solution:

This triangle is a right triangle because it satisfies the Pythagorean theorem: 6^2 + 8^2 = 10^2 (36 + 64 = 100).

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Q3. What type of triangle has all sides of different lengths?

Solution:

A triangle with all sides of different lengths is called a scalene triangle.

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Q4. What is the perimeter of a triangle with sides measuring 7 cm, 8 cm, and 9 cm?

Solution:

The perimeter of a triangle is the sum of its sides: 7 + 8 + 9 = 24 cm.

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Q5. If a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, what is the perimeter of the triangle?

Solution:

The perimeter of a triangle is the sum of its sides: 6 + 8 + 10 = 24 cm.

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Q6. In a triangle, if the lengths of the sides are 7 cm, 24 cm, and 25 cm, what type of triangle is it?

Solution:

This triangle is a right triangle because 7² + 24² = 25² (49 + 576 = 625).

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Q7. If two angles of a triangle are equal, what type of triangle is it?

Solution:

A triangle with two equal angles is called an isosceles triangle.

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Q8. If one angle of a triangle is 50 degrees and another is 60 degrees, what is the measure of the third angle?

Solution:

The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (50 + 60) = 70 degrees.

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Q9. Which of the following triangles is congruent to a triangle with sides 5 cm, 12 cm, and 13 cm?

Solution:

A triangle is congruent if it has the same side lengths. The triangle with sides 5 cm, 12 cm, and 13 cm is congruent to itself.

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Q10. If two angles of a triangle are 45 degrees and 45 degrees, what type of triangle is it?

Solution:

A triangle with two equal angles is an isosceles triangle.