Question

a square garden has a side of (x+7y)m. What would be the effect on its area if the length of each side is doubled? halved? Explain.

Answer 1

the side of the square doesn't matter for this question as long as its a square. when each side is doubled, the area will be 4 times and if halved it will be 1/4 times

Answer 2

OK the answer of your question is follows :
given that the side of the square garden is (x+7y) m . Then as You know that the area of a square = (side)*(side)
now see here
area of the square garden having (x+7y) m as side = (x+7y)m * (x+7y) m
= (x^2 + 49y^2 + 14xy )m^2
Now see the given condition says that if the side is doubled
2(x+7y)m = new side
now new area would be
(2(x+7y)m)^2 = new area
(2x+14y)^2 m^2 = new area
(4x^2 + 196y^2 + 56xy ) m^2 = new area
Now divide the new area by the old area
(4x^2 196y^2 + 56xy) / (x^2 + 49y^2 + 14xy)
4(x^2+ 49y^2 + 14xy) / (x^2 + 49y^2 + 14xy)
4/1 = 4
Hence when the side is doubled the area becomes 4 times that of previous one


Now let us see the situation when the side is halved
new side = (x+7y)/2 m
new area = (x+7y)^2/(4) m^2
= (x^2 + 49y + 14xy ) / 4 m^2
Now divide the new area by the area we got when the length of side was ( x+7y ) m
((x^2 + 49y^2 + 14xy)/4) / (x^2 + 49y^2 + 14xy)
1/4
Hence when the side of the square garden is halved then the new area would become 1/4th of the area earliest .