Question

the perimeter of an iscosel traingle is 42cm and its base is 3upon2 times of each of its equal sides .Find the length of each side of the triangle area of the triangle and the height area of the triangle and the corresponding to its longest side​

Answer 1

Answer:

∴Length of equal sides = 12cm

∴Base = 18cm

∴Height = 15cm

∴Area = 135 sq.cm

Step-by-step explanation:

Perimeter = 42cm

Let the length of equal sides be x.

Base = (3/2)x

Perimeter of isosceles triangle = base + (sum of equal sides)

                                               42 = (3/2)x + 2x

                                                42 = x [(3/2) + 2]

                                                 42 = x [7/2]

                                                  42 = (3.5)x

                                                     x = 12cm

∴Length of equal sides = 12cm

∴Base = (3/2)x = (3/2)12

                       = 18cm

∴Height = $\sqrt{9^{2} + 12^{2} }$

           = $\sqrt{81+144}$

           = $\sqrt{225}$

           = 15cm

∴Area = 1/2 X base X height

          = 1/2 X 18 X 15

          = 15 X 9

          = 135 sq.cm

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