Question

I need answers for this.

Answer 1

Answer:

• 2((4a +1) +8) cm
• 8a +18 cm
• 8a +18 = 42

Step-by-step explanation:

For the first line, you are copying the dimensions from the figure to the blanks. The dimensions on the figure are (4a +1), and (8), both in centimeters. When you have filled in that line, it will read ...

  2((4a +1) +8) cm

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For the second line, you must collect terms and use the distributive property to eliminate parentheses from the above expression.

  2((4a +1) +8) cm = 2(4a +9) cm = 2(4a) +2(9) cm

  = 8a +18 cm

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The third line simply sets this expression equal to the given perimeter, 42:

  8a +18 = 42

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Additional comment

To solve this equation, you can subtract 18 from both sides:

  8a +18 -18 = 42 -18

  8a = 24 . . . . . . . . . . . simplify

Then divide both sides by 8.

  8a/8 = 24/8

  a = 3

Finally, the length of the rectangle is ...

  4a +1 = 4(3) +1 = 12 +1 = 13

The rectangle is 13 cm long and 8 cm high. Its perimeter is ...

  2(13 +8) = 2(21) = 42 . . . cm