Total length of rectangle = 20 ft * 12 = 240 inches $$If\ \ x=45^0,$$
then the cost at which points A and C will product 2 isosceles triangle of base = 6 inches, and height = 6 inches sum of the cases of isosceles triangle = 6 + 6 = 12 inches.
The length of the rectangular board remains = 240 - 12 = 228 inches.
Given that the rectangular board has to be divided into four identical pieces, then 228 inches need to be divided equally into 4 parts.
i.e 228/4 = 57 inches.
Therefore, length AB = 57 + 6 inches ( from the base of isosceles cuts at A)
$$Length\ AB=63\ inches\ \approx5\ feet\ and\ 3\ inches$$

Answer = option C

BTGmoderatorDC wrote:

The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A, B, and C, as indicated. If x = 45, what is the length AB ? (1 foot = 12 inches)

A. 5 ft 6 in
B. 5 ft \(3\sqrt{2}\) in
C. 5 ft 3 in
D. 5 ft
E. 4 ft 9 in



OA C

Source: Official Guide

We have that

\(AB+BC=120\)
\(AB=BC+6\)

Then
\(AB=63\) inches

Therefore, __C__