Area from Perimeter 2

The aspect ratio (ratio of the width to the height) of a computer screen is 4:3. The diagonal measure is 15 inches. Find the area of the screen.

Area from Perimeter 1

The perimeter of a rectangle is 34 cm. The length is two more than twice the width. Find the area of the rectangle. Remember to show units.

Sum to 49

A right triangle has two integer sides that differ by 1. The longest side and shortest side sum to 49. Find the sides of the triangle.

Area is Perimeter

The value of a square's perimeter in inches is the same as the value of its area in square inches. What is the length of it's side?

Aspect ratio

Movies and the screens we view them on typically come in two formats. Standard format has a 3:4 aspect ratio, meaning that the picture height is ³/₄ of the picture width. Widescreen format has a 9:16 aspect ratio, so the picture height is ⁹/₁₆ of the picture width. A widescreen movie shown on a standard screen has two horizontal black bars, one above and one below the picture. Likewise, a standard movie shown on a widescreen screen has vertical black bars on the sides. What percent of the viewing area is lost to the black bars when viewing a widescreen movie on a standard screen? How about when viewing a standard movie on a widescreen screen?

Perimeter is Area

A rectangle is 3 inches longer than it is wide. The value of it's perimeter in inches is the same as the value of its area in square inches. What is the width of the rectangle?

Speed

You are in your car going 5 miles in 4 minutes. What is your speed in miles per hour?

Scones

A recipe for scones calls for 3 cups of flour and 10 tablespoons of butter and makes 12 scones. You only have 2 cups of flour, but you can still make 8 scones. How much butter should you use? (Hint: 1 tablespoon = 3 teaspoons.)

Find a Line

Find the equation of a line that passes through −3 on the y axis and 2 on the x axis.

Coin Stacks II

It is possible to mix coins in a stack to get a stack a whole number of millimeters high. For example, a stack of 2 nickels and 2 pennies has a height of exactly 2 × 1.95 + 2 × 1.55 = 7 mm. Can you find a stack of coins with a whole number of millimeters less than 7?

Coin Stacks

US coins have different thicknesses as specified below:

Penny	1.55 mm
Nickel	1.95 mm
Dime	1.35 mm
Quarter	1.75 mm

Two stacks of coins may have the same height but a different number of coins. For example, a stack of 39 pennies has a height of 39 × 1.55 = 60.45 mm, and a stack of 31 nickels also has a height of 31 × 1.95 = 60.45 mm. Find the smallest number of dimes and quarters that can likewise be made into two stacks the same height.

Circle and Square II

Which has the greater area: a 10-centimeter square, or a circle with a diameter of 11 centimeters? Explain your answer.

Circle and Square I

The diameter of a circle is the same length as the side of a square. How much greater is the area of the square?

A. It isn't greater; the circle and square have the same area.

B. The area of the square is 25% greater.

C. The area of the square is 27.3% greater.

D. The area of the square is 50% greater.

E. The area of the square is 54.6% greater.

Explain your answer.

More Odd Numbers

The sum of a sequence of odd numbers is always divisible by half of the sum of the first and last odd numbers in the sequence. For example, 7 + 9 + 11 + 13 is divisible by ½(7 + 13), and 3 + 5 + 7 + 9 + 11 is divisible by ½(3 + 11). Why?

Odd Numbers

It's been a hectic month. I am now employed again, and have had little time for word problems. However, here's a good brain teaser.

A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."

Stock Up

Walter buys shares of a stock for $1000 on Monday. On Tuesday, the stock gains 10%. On Wednesday it loses 10%. What is the value of the stock at the end of trading on Wednesday?

Twice and Thrice

The sum of two integers is twice their difference. Their product is three times their difference. What are the two integers?

Easy Does It

The ratio of two numbers is twice their sum, and their difference is zero. What are the two numbers?

Equilateral Perimeter

The perimeter of an equilateral triangle is twice the area. What is the length of a side?

Twin Triangles

Line CD is parallel to AB. What is the ratio of the area of ΔACE to ΔBDE? How do you know?