### All ACT Math Resources

## Example Questions

### Example Question #415 : Plane Geometry

The sides of rectangle A measure to , , , and . Rectangle B is similar to Rectangle A. The shorter sides of rectangle B measure each. How long are the longer sides of Rectangle B?

**Possible Answers:**

**Correct answer:**

In similar rectangles, the ratio of the sides must be equal.

To solve this question, the following equation must be set up:

, using as the variable for the missing side.

We then must cross multiply, which leaves us with:

Lastly, we divide both sides by 8 to solve for the missing side:

Therefore, the longer sides of the rectangle are each .

### Example Question #411 : Act Math

Suppose a rectangle has side lengths of 7 and 3. Another rectangle has another set of side lengths that are 8 and 4. Are these similar rectangles, and why?

**Possible Answers:**

**Correct answer:**

Set up the proportion to determine if the ratios of both rectangles are equal.

If they are, then they are similar.

These are not similar rectangles since their ratios are not the same.

### Example Question #1 : How To Find The Length Of The Diagonal Of A Quadrilateral

A square has a length of . What must be the length of the diagonal?

**Possible Answers:**

**Correct answer:**

A square with a length of indicates that all sides are since a square has 4 equal sides. Use the Pythagorean Theorem to solve for the diagonal.

### Example Question #421 : Geometry

If the rectangle has side lengths of and , what is the diagonal of the rectangle?

**Possible Answers:**

**Correct answer:**

Use the Pythagorean Theorem to solve for the diagonal.

### Example Question #1 : How To Find The Length Of The Diagonal Of A Quadrilateral

In the parallelogram above, and . What is the length of the diagonal ?

**Possible Answers:**

**Correct answer:**

In a parallelogram, the two diagonals bisect each other at their centers. Therefore, . To find , we set them equal to one another and solve.

Plugging this value back into both equations, then adding those values together, gives us our answer of .

### Example Question #1 : How To Find The Area Of A Quadrilateral

Jane plans to re-tile her kitchen with tiles that have a length of inches and a width of inches wide. If her kitchen measures feet by feet, how many tiles will she need?

**Possible Answers:**

**Correct answer:**

When attempting to solve how many pieces of a particular object you need to cover a certain area, always make sure that your units of measurement (for the object and for the area you are covering) are the same. In the case of this question, the units of measurement are different, so you must first convert all measurements to use the same unit.

Since the tiles being used to cover the area are measured in inches, convert all units given to inches:

Length: feet inches

Width: feet inches

Then, find the area of the entire space you are covering. Since the space is rectangular (this can be assumed since only length and width are given as measurements), multiply the length and width to find the total area: square inches.

Next, find the area of each of the tiles: square inches. Divide the total area of the space by the area of each of your tiles: . In cases where you are covering a certain area with an object, always round up if you have a decimal (no matter how small), because you cannot simply buy of a tile.

The answer is .

### Example Question #422 : Geometry

Vikram is looking at a scale drawing of a room he is building. The drawing is of a rectangle that measures inches by inches. If he knows the length of the longer side of the room will measure feet, what is the area of the room?

**Possible Answers:**

**Correct answer:**

When solving such problems, always make sure that your units of measurement are all the same. In the case of this problem, you must convert feet to inches. Multiply 30 by 12 in order to get its equivalent in inches.

We know that the 30 feet corresponds with the side of the drawing that is 18 inches because it is stated that the *longest* side will be 30 feet. Divide 360 by 18 in order to find the ratio of the actual size of the room to the measurements on the drawing

This means that the actual measurements of the room are 20 times the measurements of the drawing. Multiply 20 times 12 in order to find the measurement of the shorter side in inches.

Divide both the 360 and 240 by 12 to convert the measurements back into feet.

Then multiply the results to get the final answer.

### Example Question #1 : Other Quadrilaterals

If a trapezoid has base lengths of and and a height of , what is its area?

**Possible Answers:**

**Correct answer:**

Use the formula for area of a trapezoid:

Where is the area, and are the lengths of the two bases, and is the height.

In this case:

### Example Question #424 : Geometry

A parallelogram has a side length of , a height of , and a base length of . What is its area?

**Possible Answers:**

**Correct answer:**

Use the formula for area of a parallelogram:

Where is the area, is the base length, and is the height.

In this case:

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

Find the length of a rectangle if the area is , and the width is .

**Possible Answers:**

**Correct answer:**

Write the formula to solve the area of a rectangle.

Substitute the dimension and area to solve for the length.