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kolbaska11 [484]
3 years ago
10

Tracy needs to find the length and width of the equipment room where she works. The room is 2 meters longer than it is wide. The

perimeter is 16 meters. What is the width in meters?
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
8 0

Answer:

The answer to your question is: width = 3 meters

Step-by-step explanation:

Data

Perimeter = 16 meters

The room is 2 meters longer than its width, then   length = width + 2

Perimeter = 2 length + 2 width

   16 =  2(width + 2) + 2 width

    16 = 2 width + 4 + 2 width

   16 = 4 width +4

   16 - 4 = 4 width

    12 = 4 width

    12/4 = width

     3 = width  

length = 3 + 2 = 5 meters

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substitute:

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Use the Pythagorean theorem:

y^2=(17\sqrt3)^2+17^2\\\\y^2=289(\sqrt3)^2+289\\\\y^2=289\cdot3+289\\\\y^2=867+289\\\\y^2=1156\to y=\sqrt{1156}\\\\y=34

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Other method.

30^o-60^o-90^o triangle.

The sides are in the ratio 1:2:\sqrt3\to17:y:x

Therefore

17:(2\cdot17):(17\sqrt3)\to17:34:17\sqrt3\to x=34,\ y=17\sqrt3

 


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