Problem Solving

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.

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.

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%

Since 15% = 15/100 = 3/20, let the rectangle be a SQUARE with a side of 20.
Original area = s² = 20² = 400.
After each side is increased by 15% to 23, the new area = s² = 23² = 529.
Percent increase from 400 to 529 = (Difference/Smaller) * 100 = (129/400) * 100 = 129/4 = 32.25.

The correct answer is A.