Answer
a) $A = 6x^2 +28x$
b) $384 = 6x^2 +28x$
c) 6 inches, 6 inches, 13 inches
Work Step by Step
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:
$x$, $x$, $x+7$
$x=6$
$6$, $6$, $13$ ($6+7=13$)
