The area of a rhombus is 110 cm\(^2\). If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.
A
5.0
B
4.0
C
3.0
D
2.5
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Diagonal |AC| = (2x + 1)cm
In the diagram,area of \(\Delta\)ABC
is \(\frac{110}{2}\) = \(\frac{1}{2}\) x |AC| x |HB|
55 = \(\frac{1}{2}\) x (2x + 1) x 10
55 = (2x + 1)5
55 = 10x + 5
55 - 5 = 10x
50 = 10x
x = \(\frac{50}{10}\)
= 5.0
Source: Myschool Past Questions Archive (Record #45900)