Question

If a rectangle is altered by increasing its length by 20 percent and its width by 10 percent, its area increases by a percent. What is the value of a?
A) 25
B) 28
C) 30
D) 32

Answer 1

Answer:

D

Step-by-step explanation:

Remember that the formula for the area of a rectangle is:

$A=lw$

Where l is the our length and w is our width.

If we increase our length by 20%, this means that we add 20% or 0.2 of our old length to our old length. So, our new length will be:

$l_{new}=l+.2l$

Combine like terms:

$l_{new}=1.2l$

Similarly, if we increase our width by 10%, this means that we add 10% or 0.1 of our old width to our old width. So, our new width is:

$w_{new}=0.1w+w$

Combine like terms:

$w_{new}=1.1w$

Therefore, our new area will be:

$A_{new}=(l_{new})(w_{new})$

Substitute 1.2l and 1.1w. This yields:

$A_{new}=1.2l(1.1w)$

Multiply:

$A_{new}=1.32lw$

Our old area is:

$A_{old}=lw$

So, our area increased by a factor of 1.32.

This is the same as 32% of our old area.

So, our answer is D.

And we're done!