http://www.mirrormosaic.com/rectangular-mosaic-tiles/
Help two geometric three variable problems…… 10 points!!?
1. A rectangular box has a base that has a perimeter of 30cm, a side called A that has a perimeter of 24cm, and a side called B that has a perimeter of 206cm. Find the dimensions of the box.
2.A combination of tiles in the shapes shown will be used for a mosaic. The shapes chose contain a total of 40 tiles, 72 diagonals, and 153 sides. How many triangles, queares, and pentagons will be used?
remember three variable linear equations…
1. (1) 2L + 2w = 30
(2) 2w + 2h = 24
(3) 2L + 2h = 206
(1) – (3) 2L + 2w = 30
-2L – 2h = -206
(4) 2w + 2h = -176
(2) 2w + 2h = 24
4w = -152
w = -38
(1) 2L + 2w = 30
2L + 2(-38) = 30
2L = 30 + 76
2L = 106
L = 53
(2) 2w + 2h = 24
2(-38) + 2h = 24
-76 + 2h = 24
2h = 100
h = 50
2. (1)T + S + P = 40
(2) 2s + 5P = 72
(3) 3T + 4S + 5O = 153
3X(1) 3T + 3S + 3P = 120
SUBT:(4) S + 2P = 33
2X(4) 2S + 4P = 66
(2) 2S + 5P = 72
SUBT: -P = -6
P = 6
(2) 2S + 5P = 72
2S + 5(6) = 72
2S + 30 = 72
2S = 42
S = 21
(1) T + S + P = 40
T + 21 + 6 = 40
T = 13
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