Marcus and his dad were going camping. When they went into the garage to get their tent they noticed it was ripped. Marcus’s dad said he could fix the tent. He would buy some new material to cover the one rectangular side that ripped.
Part A
How much material does he need to cover the one rectangular side of the tent with the rip? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.
Part B
If Marcus’s dad wanted to re-cover the whole tent including the bottom, how much material would he need? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.
Answers
Answer:
Twelve is sixteen less than four times a number. 12 = 4x - 16.
6x + 4y = 72. (3) ... 5x − 3y = 26. (1). 4x + 2y = 34.
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Part A :
Area of rectangular side = 11 × 5 ft
= 55 ft²
Material he needs to cover the one rectangular side of the tent with the rip = 55 ft² . Ans.
Since to cover the rip in the cloth he will cover the whole side. So , the area of the cloth on the rectangular side will give the area of the cloth required to cover the rip .
Part B :
Area of the two triangles of the tent
= 2× b × h
= 2×4×6 ft²
= 48 ft²
Area of the two rectangles of the tent
= 2× b×l
= 2×5×11 ft²
= 110 ft²
Area of the two rectangles of the tent
= b×l
= 6×11 ft²
= 66 ft²
Total area of cloth required = 48 ft²+110 ft²+66 ft²
= 224 ft² Ans.
Since , Marcus’s dad wanted to re-cover the whole tent including the bottom he will require the area of cloth equal to the area of whole tent .
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