each of equal sides of an isosceles triangle is 4cm greater than its height .If the base of triangle is 24 cm ,calculate the perimeter and the area of the triangle
+128407 Let the height be = h
Each of the equal sides = sqrt [ h^2 + (base / 2) ^2 ] = sqrt [ h^2 + 12^2 ]
And we know that
sqrt [ h^2 + 12^2 ] = h + 4 square both sides
h^2 + 144 = h^2 + 8h + 16 rearrange as
144 - 16 = 8h
128 = 8h
128/8 = h = 16
So....the sides = h + 4 = 20
The perimeter = 24 + 2(20) = 68 units
The area = (1/2)base * height = (1/2) (24) (16) = 192 units^2
