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Emma wants to build a fortress wall for her LEGO castle. She will use standard LEGO bricks, which measure 3.2 cm long, 1.6 cm wide, and 0.96 cm high. Emma plans to place the bricks lengthwise in the bottom layer, with a small gap of 0.8 cm between each brick for arrow slits.
Here’s an example of the bottom layer with three bricks.
a) If Emma builds a wall with 12 layers of bricks, how tall will the fortress wall be?
b) If Emma builds a section of the wall with 8 bricks in the bottom layer, how long will this section be?
c) Emma wants one section of the fortress wall to be exactly 50 cm long. How many bricks should she use in the bottom layer of this section?
d) If Emma has a total of 250 LEGO bricks, what is the maximum length of fortress wall she can build that is 10 layers high? (Assume she uses all bricks efficiently)
a) Height of the wall with 12 layers:
12 layers × 0.96 cm per layer = 11.52 cm tall
b) Length of wall section with 8 bricks in bottom layer:
(8 bricks × 3.2 cm) + (7 gaps × 0.8 cm) = 25.6 cm + 5.6 cm = 31.2 cm long
c) For a 50 cm long section:
Let x be the number of bricks
(x × 3.2 cm) + ((x-1) × 0.8 cm) = 50 cm
3.2x + 0.8x – 0.8 = 50
4x – 0.8 = 50
4x = 50.8
x = 12.7
Since we can’t use a fraction of a brick, Emma should use 13 bricks in the bottom layer.
Actual length: (13 × 3.2) + (12 × 0.8) = 41.6 + 9.6 = 51.2 cm
d) Maximum length with 250 bricks and 10 layers high:
Bricks per layer = 250 ÷ 10 = 25 bricks
Length = (25 × 3.2 cm) + (24 × 0.8 cm) = 80 cm + 19.2 cm = 99.2 cm
The maximum length of fortress wall Emma can build is 99.2 cm or 0.992 meters.
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