Question

Q8. The perimeter of an isosceles triangle is 42 cm and its base is 1
(1/2) times each of the equal sides. Find:

1)The length of each side of the triangle.

2)The area of the triangle.

3)The height of the triangle

Answer 1

Given: The perimeter of an isosceles triangle is 42 cm and its base is 1 (1/2) times each of the equal sides.

To find: The length of each side of the triangle , the area of the triangle , the height of the triangle.

Solution:

• Now we have given that perimeter is 42 cm and base is 1(1/2) times that is 3/2 times each of the equal sides.

• Now let the equal sides be x.

• Then base will be: 3x/2

• So perimeter will be:

                x + x + 3x/2 = 42

                7x/2 = 42

                x = 12 cm.

• So the sides are 12 cm, 12 cm, and 18 cm.

• Now we know that:

                s = ( a + b + c ) / 2 = (42/2 = 21 cm

• So area of triangle by herons formula is:

                A = √(s)(s-a)(s-b)(s-c)

                A = √21(21-12)(21-12)(21-18)

                A = √21 (9) (9) (3)

                A = 27√7 cm^2

• So area = 27√7 cm^2

                1/2 × 18 × h = 27√7

                h = 27√7 × 2 / 18

               h = 3√7 cm

• So height is 3√7 cm.

Answer:

               So the length of each side of the triangle is 12 cm, 12 cm and 18 cm, the area of the triangle is 27√7 cm^2 and the height of the triangle is 3√7 cm.