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nadya68 [22]
1 year ago
5

HELP PLEASE WILL GIVE BRAINLIEST!!!

Mathematics
1 answer:
Cerrena [4.2K]1 year ago
4 0

Answer:

\fbox {Trapezoid ABCD and Trapezoid EFGH are congruent.}

Step-by-step explanation:

<u>Finding corresponding side lengths</u> :

<u>Trapezium ABCD</u>

  • AB = √(-2)² + (-1)² = √5
  • BC = √(-1)² + (2)² = √5
  • CD = √(2)² + (2)² = 2√2
  • DA = √(-1)² + (5)² = √26

<u>Trapezium EFGH</u>

  • EF = √(2)² + (1)² = √5
  • FG = √(1)² + (2)² = √5
  • GH = √(-2)² + (2)² = 2√2
  • HE = √(1)² + (5)² = √26

As the corresponding side lengths are equal, we can conclude that the trapezoids are congruent.

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Step-by-step explanation:

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2 years ago
A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a 2 feet
Ksivusya [100]

Answer:

The width and the length of the pool are 12 ft and 24 ft respectively.

Step-by-step explanation:

The length (L) of the rectangular swimming pool is twice its wide (W):

L_{1} = 2W_{1}

Also, the area of the walkway of 2 feet wide is 448:

W_{2} = 2 ft

A_{T} = W_{2}*L_{2} = 448 ft^{2}

Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle).

The total area is related to the pool area and the walkway area as follows:

A_{T} = A_{1} + A_{w}    (1)          

The area of the pool is given by:

A_{1} = L_{1}*W_{1}        

A_{1} = (2W_{1})*W_{1} = 2W_{1}^{2}  (2)          

And the area of the walkway is:

A_{w} = 2(L_{2}*2 + W_{1}*2) = 4L_{2} + 4W_{1}    (3)          

Where the length of the bigger rectangle is related to the lower rectangle as follows:                  

L_{2} = 4 + L_{1} = 4 + 2W_{1}   (4)        

By entering equations (4), (3), and (2) into equation (1) we have:

A_{T} = A_{1} + A_{w}

A_{T} = 2W_{1}^{2} + 4L_{2} + 4W_{1}                

448 = 2W_{1}^{2} + 4(4 + 2W_{1}) + 4W_{1}            

224 = W_{1}^{2} + 8 + 4W_{1} + 2W_{1}

224 = W_{1}^{2} + 8 + 6W_{1}

By solving the above quadratic equation we have:

W₁ = 12 ft

Hence, the width of the pool is 12 feet, and the length is:

L_{1} = 2W_{1} = 2*12 ft = 24 ft

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively.

I hope it helps you!                                                                                          

8 0
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Answer:

Step-by-step explanation:

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plug in the first equation

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Answer:

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I think it the second one no the 3 one you chose !
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