Question

the area of rhombus is 84cm square and its perimeter is 56cm find its height

Answer 1

Given perimeter =56cm
Area=84cm
As we know perimeter of Rhombus=4×side
therefore
56=4×side
side =56÷4
side =14
Now area= altitude×side
Altitude=Area/side
Altitude =84/14
=Altitude =6cm

Answer 2

Area of Rhombus = 1/2 (d₁+d₂) 

As Diagonal of a Rhombus splits them as equal Δs.

Then Area of Rhombus = 2 × 1/2 × bh

                                 84  = bh                                      ..................(i)
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Perimeter of Rhombus  = 4a

                                 56 = 4a

                                   a = 14 cm. (base)                     .................(ii)    
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Substituting (ii) in (i)

                                 84 = 14 × h
             
                                   h = 84 / 14

                                   h = 6 cm.
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