Increasing rectangular surface I have this problem: One side of a rectangular is lengthen by 40%. How much the other side has to be lengthen in order the surface to be bigger by 47%. The solution is given to be "by 5%". Probably the answer is simple but I don't get it. I don't understand Math at all and I have Math exam the day after tomorrow.
 A: Call the side lengths $L$ and $H$ (for length and height). You increase one side by 40%. You increase the other side by an unknown percentage. And the area increases by 47%. The area is given by the product of the length and the height, so you have
new length $\times$ new height $=$ new area $= (1 + 0.47)\times$ old area
in symbols
$$ (1+0.40)L \cdot (1 + x)H = (1+0.47) L \cdot H $$
Cancel the $L$ and $H$ from both sides, you see you need to solve
$$ 1.4 \times (1+x) = 1.47 $$
whence
$$ x = \frac{1.47}{1.4} - 1 = \frac{147 - 140}{140} = \frac{7}{140} = \frac{1}{20} = 0.05$$
So the unknown increase is 5%. 
A: Say we have a rectangle with sides $a$ and $b$.  Then the area is $ab$.  If we increase a by $40%$ we are changing it to $1.4a$ so that the area is now $1.4ab$.  Now we need to increase $b$ by some amount so that the area is $1.47ab$.  Say we multiply $b$ by and expansion factor $c$.  Then we need to find $c$ such that $1.47ab=1.4abc$ or in other words so that $$1.47=1.4c.$$  Dividing through, we see that $c=1.05$, and hence we should increase the side $b$ by $5%$.
