Question

find the area of the triangle whose sides are 30 cm 24cm 18cm also find the length of the altitude corresponding to the smallest side of the triangle ​

Answer 1

we can find the altitude with yhe help of heron's formula

here s = 24 + 18 + 30/2

72/2

=36

s=36

under square root s*(s-a)(s-b)(s-c)

under square root 36*6*12*18

answer is 216.

216 is our area of triangle

now we can easily find the height

216 = 1/2*base*height

216 = 1/2*18*h

216*2/18 = h

h = 24 cm

Answer 2

Solution :-

Given : Suppose that, Side a = 30 cm, Side b = 24 cm, Side c = 18 cm

Semi perimeter = (a + b + c)/2

= (30 + 24 + 18)/2

= 72/2 = 36 cm

By heron's formula,

Area of triangle = √{s(s - a) (s - b) (s - c)}

= √{36×(36−30)×(36−24)×(36−18)}

= √{36×6×12×18}

= √{216×12×18}

= √46656

= 216

Find the length of the altitude corresponding to the smallest side of the triangle :

Height = 2 × (Area of triangle)/(Base)

= 2 × (216)/18 cm

= 432/18 cm

= 24 cm

Hence,

Area of triangle = 216 cm²

Height = 24 cm