Roland2rule wrote:If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?
A. 32.25%
B. 40%
C. 37.50%
D. 36.75%
E. 32%
OA is C
What formula do I need for this? An Expert contribution is needed please.
Hello Roland.
There is a mistake with the answer. Let's see why.
Let's call the sides of the rectangle "x" and "y". Hence the area is A=x*y.
Now, if each side is increased by 15%, the measure of the sides will be $$X=x+15\%\cdot x=x+0.15\cdot x=1.15\cdot x$$ $$Y=y+15\%\cdot y=y+0.15\cdot y=1.15\cdot y$$ Therefore, the area of the new rectangle is $$A_2=X\cdot Y=1.15\cdot x\cdot1.15\cdot y=1.3225\cdot xy.$$ Now,
xy----------------100%
1.3225xy---------- ?
Hence, the new area represents $$\frac{1.3225xy\cdot100\%}{xy}=132.25\%\ \ \text{of}\ \text{the}\ \text{first}\ \text{area}$$ This implies that the new area is 132.25%-100% = 32.25% biger than the first rectangle.
So, the correct answer is
A.
I hope this answer may help you.
I'm available if you'd like a follow-up.
Regards.
