6th Grade Math Textbook, Fundamentals

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Problem 2:The width of a rectangle is the same as the side length
of a square. The length of the rectangle is twice the side length of the
square. The total of their areas is 588 cm^2. If the dimensions of the
figures are whole numbers, what are those dimensions?

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Lesson 1-12 for exercise sets.

Read to understand what is being asked.

List the facts and restate the question.

Facts: The width of a rectangle is the same as the side length of a square.

The length of the rectangle is twice the side length of the square.

The combined area is 588 cm^2.

Question:What are the whole-number dimensions of the square and the

rectangle in centimeters?

Select a strategy.

Because all of the involved lengths are whole numbers and

because there are only a finite number of possibilities, you

can try to find the solution using the strategy Guess and Test.

Apply the strategy.

Start by guessing the side length of the square. From this,

determine the dimensions of the rectangle, the area of each

figure, and the combined area. Based on the result, adjust

the guess and test again. Continue until you have the answer.

The table below shows one series of guesses.

The square has sides of length 14 cm, and the rectangle

has dimensions 14 cm by 28 cm.

Side Length

of Square

Width of

Rectangle

Length of

Rectangle

Area of

Square

Area of

Rectangle

Combined

Area Comment

10 10 20 100 200 300 Too low

20 20 40 400 800 1200 Too high

15 15 30 225 450 675 Too high

12 12 24 144 288 432 Too low

14 14 28 196 392 588 Correct!

Check to make sure your answer makes sense.

Draw a picture to show that the combined areas of the square and rectangle

are the same as the area of 3 of the squares.

If the side of the square is s, then its area is s^2.

3 s^2 588 cm^2 s^2  • 588 cm^2 196 cm^2 s14 cm

The width of the rectangle is s, and the length is 2s. So the

width is 14 cm, and the length is 2 • 14 cm, or 28 cm.

The dimensions are correct!

1

3

s

s

s

s

s

s ss

s

ss

s

2 s

Think

The number whose

square is 196 is 14.

(196  142 )