Question

If sides of a rhombus are 6cm each and one diagonal is 8cm, find the height of the rhombus?​

Answer 1

Step-by-step explanation:

Now we find Area of triangle ABC by Heron's formula

We know Heron's formula :

Area of triangle = s(s −a)(s −b)(s −c)−−−−−−−−−−−−−−−−−−√

Here s = a + b + c2 and a = 6 b = 6 and c = 8

So ,

s = 6 + 6 + 82 = 202 = 10 cm

Then

Area of triangle ABC = 10(10 −6)(10 −6)(10 −8)−−−−−−−−−−−−−−−−−−−−−−√ = 10 × 4 × 4 ×2−−−−−−−−−−−−−√ = 320−−−√ = 17.88 cm2

We know diagonal of rhombus divide in to two parts , So

Area of rhombus ABCD = 2 ( Area of triangle ABC ) = 2 ( 17.88 ) = 35.76 cm2

And

We know Area of rhombus = Height × side , So

Height of rhombus × 6 = 35.76

Height of rhombus = 5.96 cm ( Ans )