1. The perimeter of a rhombus is 20 m and one of its diagonal is 6m long. Find the
length of the other diagonal.
2. The sides of triangle are x,x+1,2x - 1 and its area is x 10. Find the value of n
of flower
Answers
Given : The perimeter of a rhombus is 20 m and one of its diagonal is 6m long
To Find : length of the other diagonal.
Solution:
Let say length of other diagonal = 2d m
Then rhombus side² = (diagonal1/2)² + (diagonal2/2)²
rhombus side = Perimeter/4 = 20/4 = 5 m
diagonal1/2 = 6/2 = 3 m
diagonal2/2 = 2d/2 = d m
=> 5² = 3² + d²
=> d² = 5² - 3²
=> d² = 16
=> d = 4
2d = 8
length of the other diagonal. = 8 m
The sides of triangle are x,x+1,2x - 1
s = (x + x + 1 + 2x - 1)/2 = 2x
Area = √2x(2x - x)(2x - (x + 1))(2x -(2x - 1))
= √2x.x(x - 1)1
=x√2√x - 1
x√2√x - 1 = 10x
=> 2(x - 1) = 100
=> x - 1= 50
=> x = 51
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