Question

if the area of a rhombus be 48 metre square and one of its diagonal is 12 cm find its altitude​

Answer 1

Answer:

altitude = area ÷ side  

= 48 ÷ 9.92

= 4.83 cm  

Hence, the height of the rhombus is 4.83 cm

Step-by-step explanation:

Given,

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