# 9. Define and draw the following: (2½ each) (i) Rightangle triangles (ii) Equilateral triangles (b) There are nine students in a group having ages 15, 15, 16, 16, 16, 17, 17, 18, 19 Calculate mean, medium, mode and range of their ages also define the above mentioned terms:

a) (i) A right angle triangle is a type of triangle that has one angle measuring 90 degrees, which is also known as a right angle. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem can be used to find the length of the sides of a right angle triangle, as it states that the sum of the squares of the legs is equal to the square of the hypotenuse.

(ii) An equilateral triangle is a type of triangle that has three equal sides and three equal angles, each measuring 60 degrees. The height of an equilateral triangle is the line segment drawn from the vertex to the opposite side, perpendicular to that side. The area of an equilateral triangle can be calculated using the formula A = (√3/4) × a^2, where a is the length of one of the sides.

b) To calculate the mean, median, mode, and range of the ages of the nine students in the group, we first add up all the ages and divide by nine to find the mean:

Mean = (15+15+16+16+16+17+17+18+19)/9 = 16.66

To find the median, we arrange the ages in order from smallest to largest and find the middle value. In this case, the middle value is 16, as it is the fifth value in the ordered list.

To find the mode, we look for the age that occurs most frequently in the list. In this case, the mode is 16, as it occurs three times, which is more than any other age.

To find the range, we subtract the smallest age from the largest age. In this case, the range is 19-15=4.

Mean: The average of a set of values, calculated by adding up all the values and dividing by the total number of values.

Median: The middle value in a set of ordered values, with an equal number of values above and below it.

Mode: The value that occurs most frequently in a set of values.

Range: The difference between the largest and smallest values in a set of values.