## Algebra 1

a) $A = 6x^2 +28x$ b) $384 = 6x^2 +28x$ c) 6 inches, 6 inches, 13 inches
a) $A = 2*x*x+2*(x+7)*x+2*(x+7)*x$ $A = 2x^2 +2(x^2+7x)+2(x^2+7x)$ $A = 2x^2+2x^2+14x+2x^2+14x$ $A = 6x^2 +28x$ b) $A = 2*x*x+2*x*x+2*x*x$ $A = 2x^2+2x^2+2x^2$ $A = 6x^2$ $A = 6*8^2$ $A = 6*64$ $A= 384$ c) $384 = 6x^2 +28x$ $6x^2+28x= 384$ $(6x^2+28x)/2= 384/6$ $3x^2+14x = 192$ $3x^2+14x = 192$ $(3x^2+14x = 192)/3$ $x^2+14/3*x= 64$ $x^2+14/3x+(7/3)^2=64+(7/3)^2$ $x^2+14x/3+49/9 = 64+49/9$ $(x+7/3)^2 = 576/9 + 49/9$ $(x+7/3)^2 = 625/9$ $\sqrt {(x+7/3)^2} = \sqrt {625/9}$ $(x+7/3) = ±25/3$ $x+7/3 = 25/3$ $x = 18/3$ $x= 6$ $x+7/3 = -25/3$ $x = -32/3$ We can't have a negative length, so $x=-32/3$ is not an answer. Thus, $x=6$. Dimensions: $x$, $x$, $x+7$ $x=6$ $6$, $6$, $13$ ($6+7=13$)