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Algebra Question for a 12 year old?
Having some problems explaining this to my niece (can't really work out the algebra equations myself). Would appreciate it if anyone could break it down for me, I have the answers- it's the working out that I need to show her.
The perimeter of a rectangle is 48cm. Its area is 128 cm (squared- can't find the sign). What is the length and width of the rectangle? Bear in mind that this is for a 12 year old to work out- a so called challenged question. My neighbour came up with a whole list of equations that left the poor girl confused. Please only attempt if it is simple. Answer- the length is 16cm and the width is 8cm, but using x and y could someone please break it down for me so that I can explain it to her and we can get to this answer (I looked in the back of the book). I am sure that it is simple, but it has got my mind going too. Thanks
Oh gosh that is quite complicated, but thanks. I think that I'll just about manage explaining it to her. Thanks for all of the working out!
(1) Perimeter = 2 Height + 2 Width ... or ... 2H + 2W = 48
(2) Area = Height * Width ................. or .. H*W = 128
From (1) ... 2H + 2W = 2 (H+W) = 48 ... or ... H+W =24
so ............ H = 24 - W
From (2) ... H*W = 128 ... or ... (24-W)*W = 128
so ............ 24W - W^2 = 128 ... or ... 0 = 128 + W^2 - 24W
or ............. 0 = W^2 - 24W + 128
Now what two numbers which when multiplied
together will = 128 and if added together will = -24 ?
How about -16 and -8 ?
Then (2) factors out as ... 0 = (W-16)(W-8)
Thus the answers are W=16 and W=8
Now if W=16 ... from (1) ... H = 24 - W ... or ... H = 24 - 16 ... or ... H = 8
And if W=8 ..... from (1) ... H = 24 - W ... or ... H = 24 - 8 ..... or ... H= 16
Thus either the ( Height=8 and the Width=16 ) or ( Height=16 and the Width=8 )
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