Andrew is ordering a fence, in order to make 2 new adjoining fields for some sheep. He has 8750m sq to fence and has ordered 475m of fencing supplies. Andrew wants to make the smaller field exactly three quarters the size of the larger field, and needs them both to be rectangular. What dimensions should Andrew make the blocks?
Okay, so let's start by taking out the unnecessary parts of the question.
He has 8750m sq to fence and has ordered 475 m of fencing. Andrew wants to make the smaller field exactly three quarters the size of the larger field, and needs them both to be rectangular. What dimensions should Andrew make the blocks?
I suggest you draw it out.
We know the perimeter of the rectangle must be less than 475 m. For convenience's sake, let's make one side of the field 100 m. To get the other sides, we divide 8750 by 100 to get 87.5. So now we know the dimensions of the WHOLE are 100 x 87.5 m.
Add it all together (100+100+87.5+87.5) and you get 375. He ordered 475 m of fencing, so the other 100 m must be used to divide the field (draw a line through the rectangle)
However, we still don't know how it's divided, so let's look at the rest of the question.
We know that the smaller field must be 3 quarters the size of the larger one - 1 quarter smaller.
We know that one side of both fields will still be 100 m in length, so let's work out the other length.
There are 4 quarters in a whole, so the larger field (LF) must be 4 quarters in length. The smaller field (SF) would be 3 quarters in length. Overall this is 3 + 4 which is 7 'quarters'.
Now you must divide the other side (87.5 sq m) by seven which is 12.5. So one 'quarter' is 12.5.
LF's dimensions would be 100 x 50 (in other words 12.5 x 4) making the area 5000 sq m
SF's dimensions would be 100 x 37.5 (in other words 12.5 x 3) making the area 3750 sq m
Now let's check - 50 + 37.5 is 87.5, so that should be right.
5000+ 3750 is 8750 (the original area of the field), so that should also be right.
Hope I helped
Little Miss Kingfisher - Kingfishers 11 yr old daughter.