Question

Each of equal side of an isosceles triangle is 4cm greater than its height if the base of the triangle is 24cm calculate the area of the triangle

Answer 1

Answer:

192 cm²

Step-by-step explanation:

consider height of triangle to be 'h'

thus length of side of triangle = h + 4

half length of base = 24/2 = 12

Now, consider half isoceles triangle, using Pythagoras theorem we get

(h+4)² = h² + 12²

h² + 2*4*h + 16 = h² + 12²

8*h + 16 = 144

h = (144 - 16) / 8

h = 16

Thus area = 1/2 * Base * Height

                 = 0.5 * 24 * 16

        area =  192 cm²

Answer 2

Answer:

Area = 192cm^2

Step-by-step explanation:

Base = 24cm

Height = xcm

(x+4)^2 = x^2 + (12)^2

x^2 + 8x + 16 = x^2 + (12)^2

8x = x^2 - x^2 + 144 - 16

8x = 128

x = 128/8

x = 16

Perimeter = 24 + 16+ 4 + 16 + 4

Perimeter = 64cm

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

{S = 64/2 = 32 ; A = 24 ; B = 20 ; C = 20}

Area = $\sqrt{32(32-24)(32-20)(32-20)}$

Area = $\sqrt{32*8*12*12}$

Area = $\sqrt{8*4*8*12*12}$

Area = 8*2*12

Area = $192cm^{2}$