Question

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

Answer 1

when we take rhombus figure and find the area of one of its quarter by herons formula and put it equal to half ×base×height then height get is 4√5/3cm

Answer 2

$\huge\underline\mathfrak{Answer:-}$

Let ABCD is a rhombus of side 6 cm and one diagonal AC = 8 cm.

$\bold{\boxed{\sf{\green{Perimeter\:of\:a\:triangle\:ABC}}}}$

$\sf{=(6+6+8)cm}$

$\sf{=20cm}$

s = semi-perimeter of a ∆ABC =$\sf\frac{20}{10}=10cm$

Let AB = 6cm = a, BC = 6cm = b and AC = 8cm = c

$\sf{s-a=(10-6)=4cm}$

$\sf{s-b=(10-6)=4cm}$

$\sf{s-c=(10-8)=2cm}$

So, Area of ∆ABC = $\sf\sqrt{s(s-a)(s-b)(s-c)}$

$\sf\sqrt{10\times4\times4\times2}$ cm².

$\sf{4\times2\sqrt5}$cm².

Also, area of triangle ABC = $\sf\frac{1}{2}$base*height

$\sf\frac{1}{2}$*6*height

= 3*height

From (1) and (2) we get

3*height = 8√5 cm².

Height = 8/3 √5 cm²

Hence, the height of the rhombus is 8/3 √5 cm.