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HELP Brainliest/75 points: The area of the surface of the trampoline (square) is equal to twice its perimeter. FIND THE DIMENSIONS. length= 4x ft., width= (x+6) ft.

FACTORING POLYNOMIALS/SOLVE THE EQUATION BY FACTORING HOMEWORK.

Respuesta :

gmany
If the trampoline is a square then 4x = x+6.
[tex]4x=x+6\ \ \ |-x\\3x=6\ \ \ |:3\\x=2[/tex]
therefore length = width = 4 · 2 = 8ft.
Check:
[tex]Area = 8^2=64\ ft^2\\\\twice\ Perimeter=2\cdot(4\cdot8)=2\cdot16=32\ ft\\\\Number\ of\ Area=Twice\ Number\ of\ Perimeter\\\\\to64=2\cdot32\\64=64\ OK[/tex].
If you want solve an equation.
[tex]Area=4x\cdot(x+6)=4x^2+24x\\\\Perimeter=2\cdot4x+2\cdot(x+6)=8x+2x+12=10x+12[/tex]
The Area is equal to twice Perimeter

[tex]4x^2+24x=2(10x+12)\\\\4x^2+24x=20x+24\ \ \ \ |-20x\\\\4x^2+4x=24\ \ \ |-24\\\\4x^2+4x-24=0\\\\4(x^2+x-6)=0\ \ \ |:4\\\\x^2+x-6=0\\\\x^2+3x-2x-6=0\\\\x(x+3)-2(x+3)=0\\\\(x+3)(x-2)=0\iff x+3=0\ \vee\ x-2=0\\\\x=-3 < 0\ \vee\ x=2[/tex]
Dimensions: 4x = 4 · 2 = 8ft; x + 6 = 2 + 6 = 8ft

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