### All High School Math Resources

## Example Questions

### Example Question #1 : Rectangles

The two rectangles shown below are similar. What is the length of EF?

**Possible Answers:**

10

5

6

8

**Correct answer:**

10

When two polygons are similar, the lengths of their corresponding sides are proportional to each other. In this diagram, AC and EG are corresponding sides and AB and EF are corresponding sides.

To solve this question, you can therefore write a proportion:

AC/EG = AB/EF ≥ 3/6 = 5/EF

From this proportion, we know that side EF is equal to 10.

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

A rectangle is x inches long and 3x inches wide. If the area of the rectangle is 108, what is the value of x?

**Possible Answers:**

3

12

8

6

4

**Correct answer:**

6

Solve for x

Area of a rectangle A = lw = x(3x) = 3x^{2} = 108

x^{2} = 36

x = 6

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

If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?

**Possible Answers:**

13 meters

15 meters

16 meters

14 meters

12 meters

**Correct answer:**

13 meters

Area of a rectangle is = lw

Perimeter = 2(l+w)

We are given 34 = 2(l+w) or 17 = (l+w)

possible combinations of l + w

are 1+16, 2+15, 3+14, 4+13... ect

We are also given the area of the rectangle is 52 meters squared.

Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52

Therefore the longest side of the rectangle is 13 meters

### 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 = 2l + 2

w = ½ l + 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 #1 : 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 = 6l +2

w = 1/3l +2

w = 3l + 2

w = 3l – 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 #11 : Rectangles

A rectangle has a width of and a diagonal of . What is its perimeter?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

We are given the rectangle's diagonal and width and are asked to find its perimeter. The diagonal forms two right triangles within the rectangle; therefore, we can use the Pythagorean theorem to find the length of the rectangle's missing side. Then we can use the formula to find the perimeter of the rectangle.

In our case, we can rename the variables to match our triangle.

Now we can calculate the perimeter.

### 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:**

36

32

60

81

48

**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.