### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find The Length Of The Side Of A Rectangle

The width, in cm, of a rectangular fence is 2 more than half its length, in cm. Which of the following gives the width, *w* cm, in terms of length, *l* cm, of the rectangular fence?

**Possible Answers:**

w = ½ l + 2

w = 2l + 2

w = ½ l – 2

w = 2l – 2

**Correct answer:**

w = ½ l + 2

To find the width, we must take **half of the length**, which means we must divide the length by 2. Then we must take **2 more** than that number, which means we must add 2 to the number. Combining these, we get:

*w* = ½ *l* + 2

### Example Question #2 : How To Find The Length Of The Side Of A Rectangle

The width of a rectangle is 2 inches longer than 3 times its length. Which of the following equations gives the width, w, of the rectangle in terms of its length, l,?

**Possible Answers:**

w = 3l – 2

w = 3l + 2

w = 1/3l +2

w = 6l +2

**Correct answer:**

w = 3l + 2

The width equals 3 times the length, so 3l, plus an additional two inches, so + 2, = 3l + 2

### Example Question #1 : How To Find The Length Of The Side Of A Rectangle

Your dad shows you a rectangular scale drawing of your house. The drawing is 6 inches by 8 inches. You're trying to figure out the actual length of the shorter side of the house. If you know the actual length of the longer side is 64 feet, what is the actual length of the shorter side of the house (in feet)?

**Possible Answers:**

81

48

32

60

36

**Correct answer:**

48

We can solve this by setting up a proportion and solving for x,the length of the shorter side of the house. If the drawing is scale and is 6 : 8, then the actual house is x : 64. Then we can cross multiply so that 384 = 8*x*. We then divide by 8 to get x = 48.