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
Correct Answer: Option A
Explanation
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