AIOU 248 Mathematics-II Solved Assignment 2 Spring 2025
AIOU 248 Assignment 2
Q1.(a)(10 Marks)
Q1.(b) Construct the perpendicular bisectors of the sides of a triangle. (10 Marks)
Q2.(a) The sides of a polygon are 5 cm, 2cm, 7 cm, 3 cm and 4 cm. Find the side of a similar polygon whose side corresponding to 2cm is 6cm. What is the ratio of the perimeters of these two polygons?(10 Marks)
Q2.(b) Solve the simultaneous equations by matrix inversion method where possible. Give the reason why the solution is not possible.
5x + 6y = 25
3x + 4y = 17(10 Marks)
Q3.(a) Draw an equilateral triangle, each of whose side is 8cm.(10 Marks)
Q3.(b) Define triangle. Explain different types of triangles.(10 Marks)
A triangle is a polygon with three edges (sides) and three vertices (corners). It is one of the basic shapes in geometry and consists of three connected line segments forming three angles. The sum of the interior angles of a triangle is always 180 degrees.
Types of Triangles
Classification by Sides
- Equilateral Triangle: All three sides are of equal length, and all three angles are equal, measuring 60°.
- Isosceles Triangle: Two sides are of equal length, and the angles opposite those sides are equal.
- Scalene Triangle: All three sides have different lengths, and all three angles are different.
Classification by Angles
- Acute Triangle: All three interior angles are less than 90°.
- Right Triangle: One interior angle is exactly 90°. The side opposite the right angle is called the hypotenuse.
- Obtuse Triangle: One interior angle is greater than 90°.
Fun Fact: Triangles are the simplest polygon and are often used in structural designs because of their inherent stability.
Q4.(a) Find the volume of a sphere, with a radius of 9 cm. (10 Marks)
Q4.(b) Find the hypotenuse of the right isosceles triangle, each of whose leg is 8 cm.(10 Marks)
Q5.(a) Show that the points A(6,1), B(2,7) and C(-6,7) are of a scalene triangle.(10 Marks)
Q5.(b) Find the area of the rectangle 2 m long and 20 cm wide.(10 Marks)
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