Question

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Answer 1

Area of Rhombus = 48 cm2

one diagonal = 5 cm

Area of a rhombus = fraction numerator d 1 space cross times space d 2 over denominator 2 end fraction = altitude × side

48 = fraction numerator 5 space cross times space d 2 over denominator 2 end fraction

fraction numerator 48 space cross times space 2 over denominator 5 end fraction = d2

length of diagonal 2 = 19.2 cm

We know, diagonals of a rhombus are perpendicular and bisect each other.

So, according to Pythagoras theorem,

side2 = open parentheses fraction numerator d 1 over denominator 2 end fraction close parentheses squared plus space open parentheses fraction numerator d 2 over denominator 2 end fraction close parentheses squared

= open parentheses 5 over 2 close parentheses squared plus space open parentheses fraction numerator 19.2 over denominator 2 end fraction close parentheses squared

= (2.5)2 + (9.6)2

= 6.25 + 92.16

= 98.41

side = square root of 98.41 end root space equals space 9.92

So, each side of the rhombus = 9.92 cm

altitude = area ÷ side

= 48 ÷ 9.92

= 4.83 cm

Hence, the height of the rhombus is 4.83 cm

Hope it helps...☺