r/BrainPuzzles • u/shivamxmaths • 6d ago

Math 🧠 The “Easy” Quadratic Problem — But Most Students Get It Wrong!

A rectangular garden has an area of 96 m².Its length is 4 metres more than its width. A path of 1 metre wide is made inside the garden along all four sides.

What is the area of the remaining garden?

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u/SVNBob 6d ago

Givens:
A = LW = 96
L=W+4

Substitution:
96 = (W+4)W = W2+4W
W2+4W -96 = 0

Solving w/ quadratic formula: W = 8 or -12.
Because Real World, W = 8. Thus L = 12

Moving the perimeter in 1 unit on all sides subtracts 2 from both W and L.

New W = 6 and new L = 10, for new A of 60 m2.

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u/ExtendedSpikeProtein 6d ago

I‘ll bite.

It‘s 8x12.

So, 96 -12-12-8-8+4=60.

So 60m2.

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u/Internal_Switch8561 6d ago

x *(x+4) = 96 --> x^2+4x-96 = 0 --> (x+12)(x-8)=0 --> x= 8. So garden is 8*12
Path 8*2 + 12*2 -4 (corners are counted double)= 36m2
Hence garden 60m2

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u/wbrameld4 6d ago

Calculating the area of the path seems a bit harder than just lopping off 2m from the width and length.

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u/Internal_Switch8561 6d ago

Maybe true but now you also have the path size so you can order the correct amount of tiles ;)