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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<em>Additional comment</em>
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
