Question

The perimeter of an icoceles triangle is 42 cm and its base is (3/2)times each of the equal sides .find the length of each side of the triangle, area of the triangle and the hieght of the triangle

Answer 1

Let the side of the isosceles triangle be x

GIVEN

3/2 x +x +x=42cm

3x/2 + 2x =42

(3x+4x)/2=42

3x+4x=84

7x=84

x=12cm

side=12cm base=18cm

The height(altitude) of an isos. trangle divides it into two rt trangles

in a rt.trangle, base²+heigrt²=hypotenuse²

thus, 9²+h²=12²

h=√12²-9²

=√144-81   =√63   =3√7cm

area =1/2 x base x hieght

         =1/2 x 18 x3√7 

           27√7cm²

Answer 2

Answer:

• Perimeter = 42 cm.
• The triangle given is an isosceles triangle.
• The base is 3/2 times of the other two equal sides

Find –

• All the sides.
• Area.
• Height.

Solution–

Perimeter given is 42 cm.

Hence, x + x + 3/2 x = 42

2x + 3/2 x = 42

(4x + 3x)/2 = 42

7x/2 = 42

7x = 82

x = 82/7

x = 12.

Hence, Each equal side = 12 cm.

And base = 3/2 * 12 = 3*6 = 18 cm.

Finding the area using heron's formula -

s = (12 + 12 + 18)/2 = 21 cm.

Area = √(s(s-a)(s-b)(s-c))

Area = √(21(21-12)(21-12)(21-18))

Area = √(21(9)(9)(3))

Area = √(7*(3*3)*(3*3)*(3*3))

Area = 3*3*3√(7)

Area = 27√7 cm²

Finding the height -

½ * B * H = 27√7

½ * 18 * H = 27√7

H = (27√7 * 2)/18

H = 27√7/9

Height = 3√7 cm

Conclusion -

• Height = 3√7 cm
• Equal sides = 12 cm
• Base = 18 cm
• Area = 27√7 cm