Which is the closest approximation to the area of the circle?
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Answer:
<h3>B. 4units</h3>Step-by-step explanation:
Find the diagram attached. The diagram is a similar triangle.
From the diagram, XZ/XY = CA/AB
Given XZ = 2x-2+2x-2 = 4x-4
XY =5x-7
CA = 2x-2
AB= x+1
On substituting this parameters into the formula to get x first
4x-4/5x-7 = 2x-2/x+1
cross multiply
(4x-4)(x+1) = 5x-7(2x-2)
open the parenthesis
4x²+4x-4x-4 = 10x²-10x-14x+14
4x²-4 = 10x²-24x+14
10x²-4x²-24x+14+4 = 0
6x²-24x+18 = 0
x²-4x+3 = 0
x²-3x-x+3 = 0
x(x-3)-1(x-3) =0
(x-3)(x-1) = 0
x = 3 and 1
Next is to get length AX.
Given AX = 2x-2
Substitute x = 3 into the expression
AX = 2(3)-2
AX = 6-2
AX = 4 units
Hence the measure of length AX is 4 units
