Solve
-A rope 24 feet long is cut into two unequal pieces. Each piece is used to form a square. Let x represent the length of the shorter piece of rope. Write a function $\mathrm { A } ( \mathrm { x } )$ that expresses the total area enclosed by the two squares.
A) $A ( x ) = 2 x ^ { 2 } - 48 x + 576$
B) $A ( x ) = \frac { 2 x ^ { 2 } - 48 x + 576 } { 16 }$
C) $A ( x ) = 576 - 48 x$
D) $A ( x ) = \frac { 576 - x ^ { 2 } } { 16 }$

Question

Quizplus · Accepted Answer

The total length of the rope is 24 feet. If x is the length of the shorter piece, then the longer piece is 24 - x feet. Each side of the square formed by the shorter piece is x/4, and each side of the square formed by the longer piece is (24-x)/4. The area of a square is given by the square of the side length, so the total area A(x) is $(x/4)^2 + ((24-x)/4)^2$. Simplifying this expression gives $A(x) = \frac{2x^2 - 48x + 576}{16}$, which matches choice B.

Solve -A Rope 24 Feet Long Is Cut into Two A(x)\mathrm { A } ( \mathrm { x } )A(x)

Solve
-A Rope 24 Feet Long Is Cut into Two $\mathrm { A } ( \mathrm { x } )$