**Geometry: Quadrilaterals**

*Read the following SAT test question and then select the correct answer.*

Math
questions should always be read carefully.
You will also avoid making errors by identifying the bottom line and
assessing your options for solving the question. Choose the most efficient method to attack
the problem. When you have finished,
loop back to be sure that even if there were multiple steps, you reached the
bottom line.

*The length of a rectangle is increased by 20%, and the width of the rectangle is increased by 30%. By what percentage will the area of the rectangle be increased?*

**Bottom Line**: % change = ?

**Assess your Options**: You could work this problem without picking any numbers; however, picking easy numbers will allow you to think about the problem in a more concrete way and avoid errors.

**Attack the Problem**: One of the easiest numbers to work with is one. Think of your original rectangle as having a length of one and a width of one. The formula for area of a rectangle is length times width. If L × W = A, for your first rectangle you have 1 × 1 = 1. The area of the original rectangle is one.

Then think about the
changes that occur to that rectangle.
The length increases by 20%. In
order to find 20% of 1, all you have to do is move the decimal over twice to
.2. The new length is 1.2. Use the same method to find the new width,
and an increase of 30% becomes 1.3. The
area of the rectangle after the change is 1.2 × 1.3 = 1.56

The formula for percent
change would require you to find the difference between these two areas and
divide that by the original number. You
use the same formula whether you are looking for an increase or a
decrease. Notice that your original
number is one, so dividing by one will not change your answer. All you need to do is find the difference
between the areas: 1.56 – 1 = .56. What
is .56 as a percent? Your answer is 56%.

**Loop Back**: You found the percent change, which was your bottom line. Look down at your answer choices.

(A) 25%

(B) 36%

(C) 50%

(D) 56%

(E) 60%

The correct answer is (D).

On sat.collegeboard.org, 34% of the
responses were correct.

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